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  • 1.
    Alzweighi, Mossab
    et al.
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Vehicle Engineering and Solid Mechanics, Solid Mechanics.
    Mansour, Rami
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Vehicle Engineering and Solid Mechanics, Solid Mechanics.
    Lahti, Jussi
    Graz Univ Technol, Inst Bioprod & Paper Technol, Inffeldgasse 23, A-8010 Graz, Austria.;CD Lab Fiber Swelling & Paper Performance, A-8010 Graz, Austria..
    Hirn, Ulrich
    Graz Univ Technol, Inst Bioprod & Paper Technol, Inffeldgasse 23, A-8010 Graz, Austria.;CD Lab Fiber Swelling & Paper Performance, A-8010 Graz, Austria..
    Kulachenko, Artem
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Vehicle Engineering and Solid Mechanics, Solid Mechanics. CD Lab Fiber Swelling & Paper Performance, A-8010 Graz, Austria..
    The influence of structural variations on the constitutive response and strain variations in thin fibrous materials2021In: Acta Materialia, ISSN 1359-6454, E-ISSN 1873-2453, Vol. 203, article id 116460Article in journal (Refereed)
    Abstract [en]

    The stochastic variations in the structural properties of thin fiber networks govern to a great extent their mechanical performance. To assess the influence of local structural variability on the local strain and mechanical response of the network, we propose a multiscale approach combining modeling, numerical simulation and experimental measurements. Based on micro-mechanical fiber network simulations, a continuum model describing the response at the mesoscale level is first developed. Experimentally measured spatial fields of thickness, density, fiber orientation and anisotropy are thereafter used as input to a macroscale finite-element model. The latter is used to simulate the impact of spatial variability of each of the studied structural properties. In addition, this work brings novelty by including the influence of the drying condition during the production process on the fiber properties. The proposed approach is experimentally validated by comparison to measured strain fields and uniaxial responses. The results suggest that the spatial variability in density presents the highest impact on the local strain field followed by thickness and fiber orientation. Meanwhile, for the mechanical response, the fiber orientation angle with respect to the drying restraints is the key influencer and its contribution to the anisotropy of the mechanical properties is greater than the contribution of the fiber anisotropy developed during the fiber sheet-making.

  • 2.
    Alzweighi, Mossab
    et al.
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Vehicle Engineering and Solid Mechanics, Solid Mechanics.
    Mansour, Rami
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Vehicle Engineering and Solid Mechanics, Solid Mechanics. Department of Mechanical and Production Engineering, Aarhus University, 8200 Aarhus N, Denmark.
    Maass, Alexander
    Institute of Bioproducts and Paper Technology, Graz University of Technology, Inffeldgasse 23, 8010 Graz, Austria, Inffeldgasse 23; CD Laboratory for Fiber Swelling and Paper Performance, 8010 Graz, Austria.
    Hirn, Ulrich
    Institute of Bioproducts and Paper Technology, Graz University of Technology, Inffeldgasse 23, 8010 Graz, Austria, Inffeldgasse 23; CD Laboratory for Fiber Swelling and Paper Performance, 8010 Graz, Austria.
    Kulachenko, Artem
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Vehicle Engineering and Solid Mechanics, Solid Mechanics. CD Laboratory for Fiber Swelling and Paper Performance, 8010 Graz, Austria.
    Predicting moisture penetration dynamics in paper with machine learning approach2024In: International Journal of Solids and Structures, ISSN 0020-7683, E-ISSN 1879-2146, Vol. 288, p. 112602-, article id 112602Article in journal (Refereed)
    Abstract [en]

    In this work, we predicted the gradient of the deformational moisture dynamics in a sized commercial paper by observing the curl deformation in response to the one-sided water application. The deformational moisture is a part of the applied liquid which ends up in the fibers causing swelling and subsequent mechanical response of the entire fiber network structure. The adapted approach combines traditional experimental procedures, advanced machine learning techniques and continuum modeling to provide insights into the complex phenomenon relevant to ink-jet digital printing in which the sized and coated paper is often used, meaning that not all the applied moisture will reach the fibers. Key material properties including elasticity, plastic parameters, viscoelasticity, creep, moisture dependent behavior, along with hygroexpansion coefficients are identified through extensive testing, providing vital data for subsequent simulation using a continuum model. Two machine learning models, a Feedforward Neural Network (FNN) and a Recurrent Neural Network (RNN), are probed in this study. Both models are trained using exclusively numerically generated moisture profile histories, showcasing the value of such data in contexts where experimental data acquisition is challenging. These two models are subsequently utilized to predict moisture profile history based on curl experimental measurements, with the RNN demonstrating superior accuracy due to its ability to account for temporal dependencies. The predicted moisture profiles are used as inputs for the continuum model to simulate the associated curl response comparing it to the experiment representing “never seen” data. The result of comparison shows highly predictive capability of the RNN. This study melds traditional experimental methods and innovative machine learning techniques, providing a robust technique for predicting moisture gradient dynamics that can be used for both optimizing the ink solution and paper structure to achieve desirable printing quality with lowest curl propensities during printing.

  • 3.
    Alzweighi, Mossab
    et al.
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Vehicle Engineering and Solid Mechanics, Solid Mechanics.
    Mansour, Rami
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Vehicle Engineering and Solid Mechanics, Solid Mechanics.
    Tryding, Johan
    Kulachenko, Artem
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Vehicle Engineering and Solid Mechanics, Solid Mechanics.
    Evaluation of Hoffman and Xia plasticity models against bi-axial tension experiments of planar fiber network materials2022In: International Journal of Solids and Structures, ISSN 0020-7683, E-ISSN 1879-2146, Vol. 238, article id 111358Article in journal (Refereed)
    Abstract [en]

    The anisotropic properties and pressure sensitivity are intrinsic features of the constitutive response of fiber network materials. Although advanced models have been developed to simulate the complex response of fibrous materials, the lack of comparative studies may lead to a dubiety regarding the selection of a suitable method. In this study, the pressure-sensitive Hoffman yield criterion and the Xia model are implemented for the plane stress case to simulate the mechanical response under a bi-axial loading state. The performance of both models is experimentally assessed by comparison to bi-axial tests on cruciform-shaped specimens loaded in different directions with respect to the material principal directions. The comparison with the experimentally measured forces shows the ability of the Hoffman model as well as the Xia model with shape parameter k≤2 to adequately predict the material response. However, this study demonstrates that the Xia model consistently presents a stiffer bi-axial response when k≥3 compared to the Hoffman model. This result highlights the importance of calibrating the shape parameter k for the Xia model using a bi-axial test, which can be a cumbersome task. Also, for the same tension-compression response, the Hill criterion as a special case of the Hoffman model presents a good ability to simulate the mechanical response of the material for bi-axial conditions. Furthermore, in terms of stability criteria, the Xia model is unconditionally convex while the convexity of the Hoffman model is a function of the orthotropic plastic matrix. This study not only assesses the prediction capabilities of the two models, but also gives an insight into the selection of an appropriate constitutive model for material characterization and simulation of fibrous materials. The UMAT implementations of both models which are not available in commercial software and the calibration tool of the Xia model are shared with open-source along with this work. 

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  • 4.
    Alzweighi, Mossab
    et al.
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Vehicle Engineering and Solid Mechanics, Solid Mechanics.
    Tryding, Johan
    Division of Solid Mechanics, Lund University, Ole Römers väg 1, 223 63 Lund, Sweden;Tetra Pak, Ruben Rausings gata, 221 86 Lund, Sweden.
    Mansour, Rami
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Vehicle Engineering and Solid Mechanics, Solid Mechanics. Department of Mechanical and Production Engineering, Aarhus University, 8200 Aarhus N, Denmark.
    Borgqvist, Eric
    Tetra Pak, Ruben Rausings gata, 221 86 Lund, Sweden.
    Kulachenko, Artem
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Vehicle Engineering and Solid Mechanics, Solid Mechanics.
    Anisotropic damage behavior in fiber-based materials: Modeling and experimental validation2023In: Journal of the mechanics and physics of solids, ISSN 0022-5096, E-ISSN 1873-4782, Vol. 181, article id 105430Article in journal (Refereed)
    Abstract [en]

    This study presents a thermodynamically consistent continuum damage model for fiber-based materials that combines elastoplasticity and damage mechanisms to simulate the nonlinear mechanical behavior under in-plane loading. The anisotropic plastic response is characterized by a non-quadratic yield surface composed of six sub-surfaces, providing flexibility in defining plastic properties and accuracy in reproducing material response. The damage response is modeled based on detailed uniaxial monotonic and cyclic tension-loaded experiments conducted on specimens extracted from a paper sheet in various directions. To account for anisotropic damage, we propose a criterion consisting of three sub-surfaces representing tension damage in the in-plane material principal directions and shear direction, where the damage onset is determined through cyclic loading tests. The damage evolution employs a normalized fracture energy concept based on experimental observation, which accommodates an arbitrary uniaxial loading direction. To obtain a mesh-independent numerical solution, the model is regularized using the implicit gradient enhancement by utilizing the linear heat equation solver available in commercial finite-element software. The study provides insights into the damage behavior of fiber-based materials, which can exhibit a range of failure modes from brittle-like to ductile, and establishes relationships between different length measurements.

  • 5.
    Hu, Zhangli
    et al.
    Missouri Univ Sci & Technol, Mech & Aerosp Engn, 400 West 13th St, Rolla, MO 65409 USA..
    Mansour, Rami
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Vehicle Engineering and Solid Mechanics, Solid Mechanics.
    Olsson, Mårten
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Vehicle Engineering and Solid Mechanics, Solid Mechanics.
    Du, Xiaoping
    Purdue Sch Engn & Technol, Mech & Energy Engn, 799 W Michigan St, Indianapolis, IN 46202 USA..
    Second-order reliability methods: a review and comparative study2021In: Structural and multidisciplinary optimization (Print), ISSN 1615-147X, E-ISSN 1615-1488, Vol. 64, no 6, p. 3233-3263Article, review/survey (Refereed)
    Abstract [en]

    Second-order reliability methods are commonly used for the computation of reliability, defined as the probability of satisfying an intended function in the presence of uncertainties. These methods can achieve highly accurate reliability predictions owing to a second-order approximation of the limit-state function around the Most Probable Point of failure. Although numerous formulations have been developed, the lack of full-scale comparative studies has led to a dubiety regarding the selection of a suitable method for a specific reliability analysis problem. In this study, the performance of commonly used second-order reliability methods is assessed based on the problem scale, curvatures at the Most Probable Point of failure, first-order reliability index, and limit-state contour. The assessment is based on three performance metrics: capability, accuracy, and robustness. The capability is a measure of the ability of a method to compute feasible probabilities, i.e., probabilities between 0 and 1. The accuracy and robustness are quantified based on the mean and standard deviation of relative errors with respect to exact reliabilities, respectively. This study not only provides a review of classical and novel second-order reliability methods, but also gives an insight on the selection of an appropriate reliability method for a given engineering application.

  • 6.
    Hultgren, Gustav
    et al.
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Vehicle Engineering and Solid Mechanics.
    Mansour, Rami
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Vehicle Engineering and Solid Mechanics, Solid Mechanics.
    Barsoum, Zuheir
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Vehicle Engineering and Solid Mechanics.
    Fatigue strength assessment of welded joints incorporating the variability in local weld geometry using a probabilistic framework2023In: International Journal of Fatigue, ISSN 0142-1123, E-ISSN 1879-3452, Vol. 167, article id 107364Article in journal (Refereed)
    Abstract [en]

    Progress in developing digital quality assurance systems for welded joints has made it possible to accurately measure the local geometry and its variation, making it possible to derive new relations between the geometric variations and fatigue. A probabilistic model for the fatigue strength is here presented based on the actual weld geometry. The novelty lies in that representative stresses can be determined for both the complete weld and sections of the weld. Calibration of the model using 105 fatigue-tested specimens shows a reduced variation in SN-diagrams compared with the nominal stress methods when substantial weld geometry variations are present.

  • 7.
    Hultgren, Gustav
    et al.
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics. KTH Royal Inst Technol, Lightweight Struct, Dept Engn Mech, SE-10044 Stockholm, Sweden..
    Mansour, Rami
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Vehicle Engineering and Solid Mechanics, Solid Mechanics. KTH Royal Inst Technol, Solid Mech, Dept Engn Mech, SE-10044 Stockholm, Sweden..
    Barsoum, Zuheir
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics. KTH Royal Inst Technol, Lightweight Struct, Dept Engn Mech, SE-10044 Stockholm, Sweden..
    Olsson, Mårten
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Vehicle Engineering and Solid Mechanics, Solid Mechanics. KTH Royal Inst Technol, Solid Mech, Dept Engn Mech, SE-10044 Stockholm, Sweden..
    Fatigue probability model for AWJ-cut steel including surface roughness and residual stress2021In: Journal of constructional steel research, ISSN 0143-974X, E-ISSN 1873-5983, Vol. 179, article id 106537Article in journal (Refereed)
    Abstract [en]

    An analytical model for the fatigue probability of abrasive waterjet cut high strength steel as a function of surface roughness, surface residual stress, tensile strength and number of cycles to failure is presented. Based on the model, which is valid in the finite and infinite-life high cycle fatigue regime, the influence of the aforementioned parameters on the fatigue strength at different probability levels is studied. For validation, fatigue tests are performed on abrasive waterjet-cut dog-bone specimens manufactured from high-strength steel with a yield strength of 700 MPa. Residual stresses are measured parallel to the loading direction at the inlet, middle and outlet of the cut surface. Surface roughnesses are measured with laser line triangulation as well as a traditional contact stylus method, showing good agreement between both measurement techniques. The proposed probabilistic model shows good agreement with the experimental results with less than 4% error in the predicted mean fatigue limit. Furthermore, the applicability of the presented analytical expression in a probabilistic design framework is demonstrated. An engineering example is introduced demonstrating the implementation of the model in a finite-element simulation, accounting for both multiaxial loading and the statistical size effect. (c) 2021 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY license (http:// creativecommons.org/licenses/by/4.0/).

  • 8.
    Hultgren, Gustav
    et al.
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics.
    Myrén, Leo
    Barsoum, Zuheir
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics.
    Mansour, Rami
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Vehicle Engineering and Solid Mechanics, Solid Mechanics.
    Digital scanning of welds and influence of sampling resolution on the predicted fatigue performance: modelling, experiment and simulation2021In: Metals, ISSN 2075-4701, Vol. 11, no 5, article id 822Article in journal (Refereed)
    Abstract [en]

    Digital weld quality assurance systems are increasingly used to capture local geometrical variations that can be detrimental for the fatigue strength of welded components. In this study, a method is proposed to determine the required scanning sampling resolution for proper fatigue assessment. Based on FE analysis of laser‐scanned welded joints, fatigue failure probabilities are computed using a Weakest‐link fatigue model with experimentally determined parameters. By down‐sampling of the scanning data in the FE simulations, it is shown that the uncertainty and error in the fatigue failure probability prediction increases with decreased sampling resolution. The required sampling resolution is thereafter determined by setting an allowable error in the predicted failure probability. A sampling resolution of 200 to 250 μm has been shown to be adequate for the fatigue‐loaded welded joints investigated in the current study. The resolution requirements can be directly incorporated in production for continuous quality assurance of welded structures. The proposed probabilistic model used to derive the resolution requirement accurately captures the experimental fatigue strength distribution, with a correlation coefficient of 0.9 between model and experimental failure probabilities. This work therefore brings novelty by deriving sampling resolution requirements based on the influence of stochastic topographical variations on the fatigue strength distribution. 

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  • 9.
    Mansour, Rami
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Solid Mechanics (Div.).
    Development of efficient and accurate methods for Reliability-based Design Optimization2014Licentiate thesis, comprehensive summary (Other academic)
  • 10.
    Mansour, Rami
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Solid Mechanics (Div.).
    Reliability Assessment and Probabilistic Optimization in Structural Design2016Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    Research in the field of reliability based design is mainly focused on two sub-areas: The computation of the probability of failure and its integration in the reliability based design optimization (RBDO) loop. Four papers are presented in this work, representing a contribution to both sub-areas. In the first paper, a new Second Order Reliability Method (SORM) is presented. As opposed to the most commonly used SORMs, the presented approach is not limited to hyper-parabolic approximation of the performance function at the Most Probable Point (MPP) of failure. Instead, a full quadratic fit is used leading to a better approximation of the real performance function and therefore more accurate values of the probability of failure. The second paper focuses on the integration of the expression for the probability of failure for general quadratic function, presented in the first paper, in RBDO. One important feature of the proposed approach is that it does not involve locating the MPP. In the third paper, the expressions for the probability of failure based on general quadratic limit-state functions presented in the first paper are applied for the special case of a hyper-parabola. The expression is reformulated and simplified so that the probability of failure is only a function of three statistical measures: the Cornell reliability index, the skewness and the kurtosis of the hyper-parabola. These statistical measures are functions of the First-Order Reliability Index and the curvatures at the MPP. In the last paper, an approximate and efficient reliability method is proposed. Focus is on computational efficiency as well as intuitiveness for practicing engineers, especially regarding probabilistic fatigue problems where volume methods are used. The number of function evaluations to compute the probability of failure of the design under different types of uncertainties is a priori known to be 3n+2 in the proposed method, where n is the number of stochastic design variables.

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    Thesis
  • 11.
    Mansour, Rami
    et al.
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Vehicle Engineering and Solid Mechanics, Solid Mechanics.
    Gillgren, Sara
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Vehicle Engineering and Solid Mechanics, Solid Mechanics.
    Dadbakhsh, Sasan
    KTH, School of Industrial Engineering and Management (ITM), Production Engineering, Manufacturing and Metrology Systems.
    Topology Optimization for Additive Manufacturing – A Numerical Study of Current Design Framework Capabilities and Limitations2022In: Advances in Transdisciplinary Engineering / [ed] A.H.C. Ng et al., IOS Press , 2022, Vol. 21, p. 592-603Conference paper (Refereed)
    Abstract [en]

    Topology optimization (TO) is commonly used to minimize the weight of a structural component subject to a constraint on the maximum equivalent stress. In TO for additive manufacturing (AM), constraints on the build direction as well as the overhang angle are also included in the optimization. However, current design framework generally doesn’t include the residual stresses and distortions that result from the AM process directly into the TO. In this work, it is shown that this limitation can result in components that may fail during the Selective Laser Melting (SLM) due to high stresses and distortion that were not accounted for in the TO. For the studied demonstrative bracket design from Ti-6Al-4V, it is shown that the spatial stress distribution, including both the location and magnitude of the maximum stress, is strongly altered after SLM compared to the stresses used in the TO, even after heat treatment. This work highlights the importance of integrating AM process simulation with residual stress and distortion prediction directly in the TO, which is currently a difficult and computationally inefficient task.

  • 12.
    Mansour, Rami
    et al.
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Vehicle Engineering and Solid Mechanics, Solid Mechanics.
    Kulachenko, Artem
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Vehicle Engineering and Solid Mechanics, Solid Mechanics.
    Stochastic constitutive model of thin fibre networks2022In: Mechanics of Fibrous Networks / [ed] Vadim V. Silberschmidt, Elsevier, 2022, p. 75-112Chapter in book (Refereed)
    Abstract [en]

    Thin fibre networks are characterised by a certain degree of randomness in their mechanical response. This randomness can be seen as one of the main reasons for unexplained occasional failures that cannot be predicted by deterministic materials models. Direct fibre-level mechanical simulations can provide insights into the role of the constitutive components of such networks as well as capture the mechanisms of failure. However, these direct simulations are limited to small fibre networks due to overwhelming computational costs and cannot be employed for product development. Therefore, a stochastic multiscale approach for predicting the random mechanical response for thin fibre networks of arbitrary size is necessary. In such a model, the randomness in the network is mathematically described by spatial fields of material properties characterised using stochastic volume elements. In this book chapter, the steps involved in three-dimensional (3D)-fibre network characterisation, random generation, and finite-element simulation are described. This is followed by a description of the stochastic continuum modelling approach with a quantitative comparison to direct numerical simulation with respect to mechanical response and strain localisation pattern. The mathematical preliminaries and advanced topics related to stochastic continuum modelling using spatial field representations are presented in detail.

  • 13.
    Mansour, Rami
    et al.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
    Kulachenko, Artem
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Solid Mechanics (Div.).
    Chen, W.
    Olsson, Mårten
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
    Stochastic constitutive model of isotropic thin fiber networks based on stochastic volume elements2019In: Materials, E-ISSN 1996-1944, Vol. 12, no 3, article id 538Article in journal (Refereed)
    Abstract [en]

    Thin fiber networks are widely represented in nature and can be found in man-made materials such as paper and packaging. The strength of such materials is an intricate subject due to inherited randomness and size-dependencies. Direct fiber-level numerical simulations can provide insights into the role of the constitutive components of such networks, their morphology, and arrangements on the strength of the products made of them. However, direct mechanical simulation of randomly generated large and thin fiber networks is characterized by overwhelming computational costs. Herein, a stochastic constitutive model for predicting the random mechanical response of isotropic thin fiber networks of arbitrary size is presented. The model is based on stochastic volume elements (SVEs) with SVE size-specific deterministic and stochastic constitutive law parameters. The randomness in the network is described by the spatial fields of the uniaxial strain and strength to failure, formulated using multivariate kernel functions and approximate univariate probability density functions. The proposed stochastic continuum approach shows good agreement when compared to direct numerical simulation with respect to mechanical response. Furthermore, strain localization patterns matched the one observed in direct simulations, which suggests an accurate prediction of the failure location. This work demonstrates that the proposed stochastic constitutive model can be used to predict the response of random isotropic fiber networks of arbitrary size.

  • 14.
    Mansour, Rami
    et al.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Solid Mechanics (Div.).
    Olsson, Mårten
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Solid Mechanics (Div.).
    A Closed-Form Second-Order Reliability Method Using Noncentral Chi-Squared Distributions2014In: Journal of mechanical design (1990), ISSN 1050-0472, E-ISSN 1528-9001, Vol. 136, no 10, p. 101402-Article in journal (Refereed)
    Abstract [en]

    In the second-order reliability method (SORM), the probability of failure is computed for an arbitrary performance function in arbitrarily distributed random variables. This probability is approximated by the probability of failure computed using a general quadratic fit made at the most probable point (MPP). However, an easy-to-use, accurate, and efficient closed-form expression for the probability content of the general quadratic surface in normalized standard variables has not yet been presented. Instead, the most commonly used SORM approaches start with a relatively complicated rotational transformation. Thereafter, the last row and column of the rotationally transformed Hessian are neglected in the computation of the probability. This is equivalent to approximating the probability content of the general quadratic surface by the probability content of a hyperparabola in a rotationally transformed space. The error made by this approximation may introduce unknown inaccuracies. Furthermore, the most commonly used closed-form expressions have one or more of the following drawbacks: They neither do work well for small curvatures at the MPP and/or large number of random variables nor do they work well for negative or strongly uneven curvatures at the MPP. The expressions may even present singularities. The purpose of this work is to present a simple, efficient, and accurate closed-form expression for the probability of failure, which does not neglect any component of the Hessian and does not necessitate the rotational transformation performed in the most common SORM approaches. Furthermore, when applied to industrial examples where quadratic response surfaces of the real performance functions are used, the proposed formulas can be applied directly to compute the probability of failure without locating the MPP, as opposed to the other first-order reliability method (FORM) and the other SORM approaches. The method is based on an asymptotic expansion of the sum of noncentral chi-squared variables taken from the literature. The two most widely used SORM approaches, an empirical SORM formula as well as FORM, are compared to the proposed method with regards to accuracy and computational efficiency. All methods have also been compared when applied to a wide range of hyperparabolic limit-state functions as well as to general quadratic limit-state functions in the rotationally transformed space, in order to quantify the error made by the approximation of the Hessian indicated above. In general, the presented method was the most accurate for almost all studied curvatures and number of random variables.

  • 15.
    Mansour, Rami
    et al.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Solid Mechanics (Div.).
    Olsson, Mårten
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Solid Mechanics (Div.).
    A novel closed-form Second-Order Reliability Method with probabilistic sensitivity analysis and application in Reliability-based Design Optimization2016Report (Other academic)
  • 16.
    Mansour, Rami
    et al.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Solid Mechanics (Div.).
    Olsson, Mårten
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Solid Mechanics (Div.).
    An efficient reliability method applied to classical load-strength uncertainties, aleatory fatigue problems and epistemic uncertainties2016Report (Other academic)
  • 17.
    Mansour, Rami
    et al.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
    Olsson, Mårten
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
    Efficient Reliability Assessment With the Conditional Probability Method2018In: Journal of mechanical design (1990), ISSN 1050-0472, E-ISSN 1528-9001, Vol. 140, no 8, article id 081402Article in journal (Refereed)
    Abstract [en]

    Reliability assessment is an important procedure in engineering design in which the probability of failure or equivalently the probability of survival is computed based on appropriate design criteria and model behavior. In this paper, a new approximate and efficient reliability assessment method is proposed: the conditional probability method (CPM). Focus is set on computational efficiency and the proposed method is applied to classical load-strength structural reliability problems. The core of the approach is in the computation of the probability of failure starting from the conditional probability of failure given the load. The number of function evaluations to compute the probability of failure is a priori known to be 3n+2 in CPM, where n is the number of stochastic design variables excluding the strength. The necessary number of function evaluations for the reliability assessment, which may correspond to expensive computations, is therefore substantially lower in CPM than in the existing structural reliability methods such as the widely used first-order reliability method (FORM).

  • 18.
    Mansour, Rami
    et al.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Solid Mechanics (Div.).
    Olsson, Mårten
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Solid Mechanics (Div.).
    Response surface single loop reliability-based design optimization with higher order reliability assessmentManuscript (preprint) (Other academic)
  • 19.
    Mansour, Rami
    et al.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Solid Mechanics (Div.).
    Olsson, Mårten
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Solid Mechanics (Div.).
    Response surface single loop reliability-based design optimization with higher-order reliability assessment2016In: Structural and multidisciplinary optimization (Print), ISSN 1615-147X, E-ISSN 1615-1488, p. 1-17Article in journal (Refereed)
    Abstract [en]

    Reliability-based design optimization (RBDO) aims at determination of the optimal design in the presence of uncertainty. The available Single-Loop approaches for RBDO are based on the First-Order Reliability Method (FORM) for the computation of the probability of failure, along with different approximations in order to avoid the expensive inner loop aiming at finding the Most Probable Point (MPP). However, the use of FORM in RBDO may not lead to sufficient accuracy depending on the degree of nonlinearity of the limit-state function. This is demonstrated for an extensively studied reliability-based design for vehicle crashworthiness problem solved in this paper, where all RBDO methods based on FORM strongly violates the probabilistic constraints. The Response Surface Single Loop (RSSL) method for RBDO is proposed based on the higher order probability computation for quadratic models previously presented by the authors. The RSSL-method bypasses the concept of an MPP and has high accuracy and efficiency. The method can solve problems with both constant and varying standard deviation of design variables and is particularly well suited for typical industrial applications where general quadratic response surface models can be used. If the quadratic response surface models of the deterministic constraints are valid in the whole region of interest, the method becomes a true single loop method with accuracy higher than traditional SORM. In other cases, quadratic response surface models are fitted to the deterministic constraints around the deterministic solution and the RBDO problem is solved using the proposed single loop method.

  • 20.
    Mansour, Rami
    et al.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Solid Mechanics (Div.).
    Olsson, Mårten
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Solid Mechanics (Div.).
    Second-order reliability method based on Edgeworth expansion with application to reliability-based design optimization2019In: Proceedings of the ASME Design Engineering Technical Conference, ASME International , 2019Conference paper (Refereed)
    Abstract [en]

    In the Second-Order Reliability Method, the limit-state function is approximated by a hyper-parabola in standard normal and uncorrelated space. However, there is no exact closed form expression for the probability of failure based on a hyper-parabolic limit-state function and the existing approximate formulas in the literature have been shown to have major drawbacks. Furthermore, in applications such as Reliability-based Design Optimization, analytical expressions, not only for the probability of failure but also for probabilistic sensitivities, are highly desirable for efficiency reasons. In this paper, a novel Second-Order Reliability Method is presented. The proposed expression is a function of three statistical measures: the Cornell Reliability Index, the skewness and the Kurtosis of the hyper-parabola. These statistical measures are functions of the First-Order Reliability Index and the curvatures at the Most Probable Point. Furthermore, analytical sensitivities with respect to mean values of random variables and deterministic variables are presented. The sensitivities can be seen as the product of the sensitivities computed using the First-Order Reliability Method and a correction factor. The proposed expressions are studied and their applicability to Reliability-based Design Optimization is demonstrated.

  • 21.
    Mansour, Rami
    et al.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
    Olsson, Mårten
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
    The response surface single loop reliability-based design optimization method with reliability requirement on system failure2016In: Proceedings of the ASME Design Engineering Technical Conference, American Society of Mechanical Engineers (ASME) , 2016Conference paper (Refereed)
    Abstract [en]

    In reliability-based design optimization (RBDO), an optimal design which minimizes an objective function while satisfying a number of probabilistic constraints is found. As opposed to deterministic optimization, statistical uncertainties in design variables and design parameters have to be taken into account in the design process in order to achieve a reliable design. In the most widely used RBDO approaches, the First-Order Reliability Method (FORM) is used in the probability assessment. This involves locating the Most Probable Point (MPP) of failure, or the inverse MPP, either exactly or approximately. If exact methods are used, an optimization problem has to be solved, typically resulting in computationally expensive double loop or decoupled loop RBDO methods. On the other hand, locating the MPP approximately typically results in highly efficient single loop RBDO methods since the optimization problem is not necessary in the probability assessment. However, since all these methods are based on FORM, which in turn is based on a linearization of the deterministic constraints at the MPP, they may suffer inaccuracies associated with neglecting the nonlinearity of deterministic constraints. In a previous paper presented by the authors, the Response Surface Single Loop (RSSL) Reliability-based design optimization method was proposed. The RSSL-method takes into account the non-linearity of the deterministic constraints in the computation of the probability of failure and was therefore shown to have higher accuracy than existing RBDO methods. The RSSL-method was also shown to have high efficiency since it bypasses the concept of an MPP. In RSSL, the deterministic solution is first found by neglecting uncertainties in design variables and parameters. Thereafter quadratic response surface models are fitted to the deterministic constraints around the deterministic solution using a single set of design of experiments. The RBDO problem is thereafter solved in a single loop using a closed-form second order reliability method (SORM) which takes into account all elements of the Hessian of the quadratic constraints. In this paper, the RSSL method is used to solve the more challenging system RBDO problems where all constraints are replaced by one constraint on the system probability of failure. The probabilities of failure for the constraints are assumed independent of each other. In general, system reliability problems may be more challenging to solve since replacing all constraints by one constraint may strongly increase the non-linearity in the optimization problem. The extensively studied reliability-based design for vehicle crash-worthiness, where the provided deterministic constraints are general quadratic models describing the system in the whole region of interest, is used to demonstrate the capabilities of the RSSL method for problems with system reliability constraints.

  • 22.
    Mansour, Rami
    et al.
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Vehicle Engineering and Solid Mechanics, Solid Mechanics.
    Zhu, Jinchao
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Vehicle Engineering and Solid Mechanics, Solid Mechanics.
    Edgren, Martin
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Vehicle Engineering and Solid Mechanics, Solid Mechanics. DEKRA Industrial AB, SE-171 54, Solna, Sweden.
    Barsoum, Zuheir
    KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering.
    A probabilistic model of weld penetration depth based on process parameters2019In: The International Journal of Advanced Manufacturing Technology, ISSN 0268-3768, E-ISSN 1433-3015, Vol. 105, no 1-4, p. 499-514Article in journal (Refereed)
    Abstract [en]

    In welded structures using robotized metal active gas (MAG) welding, unwanted variation in penetration depth is typically observed. This is due to uncertainties in the process parameters which cannot be fully controlled. In this work, an analytical probabilistic model is developed to predict the probability of satisfying a target penetration, in the presence of these uncertainties. The proposed probabilistic model incorporates both aleatory process parameter uncertainties and epistemic measurement uncertainties. The latter is evaluated using a novel digital tool for weld penetration measurement. The applicability of the model is demonstrated on fillet welds based on an experimental investigation. The studied input process parameters are voltage, current, travel speed, and torch travel angle. The uncertainties in these parameters are modelled using adequate probability distributions and a statistical correlation based on the volt-ampere characteristic of the power source. Using the proposed probabilistic model, it is shown that a traditional deterministic approach in setting the input process parameters typically results in only a 50% probability of satisfying a target penetration level. It is also shown that, using the proposed expressions, process parameter set-ups satisfying a desired probability level can be simply identified. Furthermore, the contribution of the input uncertainties to the variation of weld penetration is quantified. This work paves the way to make effective use of the robotic welding, by targeting a specified probability of satisfying a desired weld penetration depth as well as predicting its variation.

  • 23.
    Sandberg, Daniel
    et al.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
    Mansour, Rami
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
    Olsson, Mårten
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
    Fatigue probability assessment including aleatory and epistemic uncertainty with application to gas turbine compressor blades2017In: International Journal of Fatigue, ISSN 0142-1123, E-ISSN 1879-3452, Vol. 95, p. 132-142Article in journal (Refereed)
    Abstract [en]

    In, this work, a new method for fatigue probability assessment is introduced. The method is applied to a bladed disk in a gas turbine for computation of the high cycle fatigue probability. Both epistemic and aleatory uncertainties are modeled. The aleatory uncertainty is of two types: Variable aleatory uncertainty is modeled by use of stochastic variables that influence the problem, including both design variables and stochastic parameters. Physical aleatory uncertainty is modeled by use of a probability that remains even if all stochastic variables are replaced by deterministic values. The fatigue behavior of a material exhibits physical aleatory uncertainty. The results show that the epistemic uncertainty in the modeling of the aero-forcing gives the major contribution to uncertainty in the computed failure probability. The new method is also used to study the influence on the probability of high cycle fatigue that comes from the stochastic variables.

  • 24.
    Sandberg, Daniel
    et al.
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Solid Mechanics (Div.).
    Mansour, Rami
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Solid Mechanics (Div.).
    Olsson, Mårten
    KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Solid Mechanics (Div.).
    Probabilistic fatigue design of gas turbine compressor blades under aleatory and epistemic uncertainty2016Report (Other academic)
    Abstract [en]

    In this work, a new method for fatigue probability assessment is introduced. The method is applied to a bladed disk in a gas turbine for computation of the fatigue probability for a specific load case. Both epistemic and aleatory uncertainties are modeled. The aleatory uncertainty is of two types: Type 1 aleatory uncertainty is modeled by use of stochastic variables that influence the problem, including both design variables and stochastic parameters. Type 2 aleatory uncertainty is modeled by use of a probability that remains even if all stochastic variables are replaced by deterministic values. The fatigue behavior of a material exhibits type 2 aleatory uncertainty. The results show that the epistemic uncertainty in the modeling of the aero-forcing and the damping gives a large uncertainty in the computed failure probability. The new method is also used to study the influence on the probability of fatigue that comes from the stochastic variables.

  • 25.
    Subasic, Mustafa
    et al.
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Material and Structural Mechanics.
    Ireland, Aaron
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Material and Structural Mechanics.
    Mansour, Rami
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Material and Structural Mechanics. Department of Mechanical and Production Engineering, Aarhus University, 8200 Aarhus N, Denmark.
    Enblom, Peter
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Material and Structural Mechanics.
    Krakhmalev, P.
    cDepartment of Engineering and Physics, Karlstads University, SE-651 88 Karlstad, Sweden.
    Åsberg, M.
    cDepartment of Engineering and Physics, Karlstads University, SE-651 88 Karlstad, Sweden.
    Fazi, A.
    dDepartment of Physics, Chalmers University of Technology, SE-412 96 Gothenburg, Sweden.
    Gårdstam, J.
    eQuintus Technologies AB, SE-721 36 Västerås, Sweden.
    Shipley, J.
    eQuintus Technologies AB, SE-721 36 Västerås, Sweden.
    Waernqvist, P.
    fRinghals AB, Ringhalsverket, SE-432 85 Väröbacka, Sweden.
    Forssgren, B.
    fRinghals AB, Ringhalsverket, SE-432 85 Väröbacka, Sweden.
    Efsing, Pål
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Material and Structural Mechanics. Ringhals AB, Ringhalsverket, SE-432 85 Väröbacka, Sweden.
    Experimental investigation and numerical modelling of the cyclic plasticity and fatigue behavior of additively manufactured 316 L stainless steel2024In: International journal of plasticity, ISSN 0749-6419, E-ISSN 1879-2154, Vol. 176, article id 103966Article in journal (Refereed)
    Abstract [en]

    This study addresses the critical need for a constitutive model to analyze the cyclic plasticity of additively manufactured 316L stainless steel. The anisotropic behavior at both room temperature and 300 °C is investigated experimentally based on cyclic hysteresis loops performed in different orientations with respect to the build direction. A comprehensive constitutive model is proposed, that integrates the Armstrong-Frederick nonlinear kinematic hardening, Voce nonlinear isotropic hardening and Hill's anisotropic yield criterion within a 3D return mapping algorithm. The model was calibrated to specimens in the 0° and 90° orientations and validated with specimens in the 45° orientation. A single set of hardening parameters successfully represented the elastoplastic response for all orientations at room temperature. The algorithm effectively captured the full cyclic hysteresis loops, including historical effects observed in experimental tests. A consistent trend of reduced hardening was observed at elevated temperature, while the 45° specimen orientation consistently exhibited the highest degree of strain hardening. The applicability of the model was demonstrated by computing energy dissipation for stabilized hysteresis loops, which was combined with fatigue tests to propose an energy-based fatigue life prediction model.

  • 26.
    Subasic, Mustafa
    et al.
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Vehicle Engineering and Solid Mechanics, Solid Mechanics.
    Olsson, Mårten
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Vehicle Engineering and Solid Mechanics, Solid Mechanics.
    Dadbakhsh, Sasan
    KTH, School of Industrial Engineering and Management (ITM), Production engineering, Manufacturing and Metrology Systems.
    Zhao, Xiaoyu
    KTH, School of Industrial Engineering and Management (ITM), Production engineering, Manufacturing and Metrology Systems.
    Krakhmalev, Pavel
    Department of Engineering and Physics, Karlstad University, 651 88 Karlstad, Sweden.
    Mansour, Rami
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Vehicle Engineering and Solid Mechanics, Solid Mechanics. Department of Mechanical and Production Engineering, Aarhus University, 8200 Aarhus N, Denmark; DIGIT Center, 8200 Aarhus N, Denmark.
    Fatigue strength improvement of additively manufactured 316L stainless steel with high porosity through preloading2024In: International Journal of Fatigue, ISSN 0142-1123, E-ISSN 1879-3452, Vol. 180, article id 108077Article in journal (Refereed)
    Abstract [en]

    This work investigates the influence of a single tensile preload, applied prior to fatigue testing, on the fatigue strength of 316L stainless steel parts manufactured using laser-based powder bed fusion (PBF-LB) with a porosity of up to 4 %. The specimens were produced in both the horizontal and vertical build directions and were optionally preloaded to 85 % and 110 % of the yield strength before conducting the fatigue tests. The results indicate a clear tendency of improved fatigue life and fatigue limit with increasing overload in both cases. The fatigue limits increased by 25.8 % and 24.6 % for the horizontally and vertically built specimens, respectively. Extensive modelling and experiments confirmed that there was no significant alteration in the shape and size of the porosity before and after preloading. Therefore, the observed enhancement in fatigue performance was primarily attributed to the imposed local compressive residual stresses around the defects.

  • 27.
    Zhao, Xiaoyu
    et al.
    KTH, School of Industrial Engineering and Management (ITM), Production engineering, Manufacturing and Metrology Systems.
    Wei, Yuan
    Northwestern Polytech Univ, Xian Inst Flexible Elect IFE, Xian Inst Biomed Mat & Engn, Frontiers Sci Ctr Flexible Elect, Xian 710072, Peoples R China..
    Mansour, Rami
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Vehicle Engineering and Solid Mechanics, Solid Mechanics.
    Dadbakhsh, Sasan
    KTH, School of Industrial Engineering and Management (ITM), Production engineering, Manufacturing and Metrology Systems.
    Rashid, Amir
    KTH, School of Industrial Engineering and Management (ITM), Production engineering, Manufacturing and Metrology Systems.
    Effect of Scanning Strategy on Thermal Stresses and Strains during Electron Beam Melting of Inconel 625: Experiment and Simulation2023In: Materials, E-ISSN 1996-1944, Vol. 16, no 1, article id 443Article in journal (Refereed)
    Abstract [en]

    This paper develops a hybrid experimental/simulation method for the first time to assess the thermal stresses generated during electron beam melting (EBM) at high temperatures. The bending and rupture of trusses supporting Inconel 625 alloy panels at similar to 1050 degrees C are experimentally measured for various scanning strategies. The generated thermal stresses and strains are thereafter simulated using the Finite-Element Method (FEM). It is shown that the thermal stresses on the trusses may reach the material UTS without causing failure. Failure is only reached after the part experiences a certain magnitude of plastic strain (similar to 0.33 +/- 0.01 here). As the most influential factor, the plastic strain increases with the scanning length. In addition, it is shown that continuous scanning is necessary since the interrupted chessboard strategy induces cracking at the overlapping regions. Therefore, the associated thermal deformation is to be minimized using a proper layer rotation according to the part length. Although this is similar to the literature reported for selective laser melting (SLM), the effect of scanning pattern is found to differ, as no significant difference in thermal stresses/strains is observed between bidirectional and unidirectional patterns from EBM.

  • 28.
    Zhao, Xiaoyu
    et al.
    KTH, School of Industrial Engineering and Management (ITM), Production Engineering, Manufacturing and Metrology Systems.
    Yuan, Wei
    Northwestern Polytechnical University, 127 Youyi W Rd, Bian Jia Cun Shang Ye Jie Qu, Beilin, Xi'an, Shaanxi, China.
    Mansour, Rami
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Vehicle Engineering and Solid Mechanics, Solid Mechanics.
    Dadbakhsh, Sasan
    KTH, School of Industrial Engineering and Management (ITM), Production Engineering, Manufacturing and Metrology Systems.
    Rashid, Amir
    KTH, School of Industrial Engineering and Management (ITM), Production Engineering, Manufacturing and Metrology Systems.
    Effect of scanning strategy on thermal stresses and strains during electron beam melting of Inconel 625: experiment and simulation2022In: Article in journal (Other academic)
  • 29.
    Zhu, Jinchao
    et al.
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Vehicle Engineering and Solid Mechanics, Lightweight Structures.
    Barsoum, Zuheir
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Vehicle Engineering and Solid Mechanics, Lightweight Structures.
    Mansour, Rami
    KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Vehicle Engineering and Solid Mechanics, Solid Mechanics.
    Numerical study of the influence of weld geometry variations on fatigue life using the notch stress analysis2022Conference paper (Refereed)
    Abstract [en]

    Idealized geometry is typically used in standards for the fatigue life assessment of welded joints. In the presence of stochastic geometrical variations along the weld, the choice of the idealized geometry is however ambiguous. In the notch stress (NS) method with a fictitious notch radius rref = 1 mm, the FAT 225 curve is derived for welds with relatively good quality in toe profiles. In the NS method with rref = ractual + 1 mm, a lower FAT 200 curve is recommended. Both approaches neglect the stochastic variability in toe radius, toe angle and leg length along the weld. The aim of this paper is two-fold. First, a numerical comparison between both approaches in terms of their predicted fatigue life is performed for a non-load carrying fillet cruciform joints. The results show that the NS method with rref = 1 mm and FAT 225 is substantially more conservative. Second, these methods are enhanced by replacing the deterministic stress concentration factor by a probability distribution computed using Monte Carlo simulation. It is shown that NS with rref = 1 mm and FAT 225 does not predict any substantial influence of the stochastic variability in process parameters since the actual toe radius is not included in the analysis. However, the NS method with rref = ractual + 1 mm and FAT 200 predicts a decrease in fatigue life when uncertainties in geometrical parameters is included. This numerical study paves the way for an experimental validation of the predicted influence of stochastic variability of geometrical parameters based on the stochastic notch stress analysis.

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