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Abstract: This paper unravels an intrinsic shortcoming of several cohesive zone models, whereby commonly adopted traction separation laws do not necessarily satisfy rotational equilibrium at the cohesive element level. The necessary condition to ensure rotational equilibrium is derived. To demonstrate the error that is caused by the lack of rotational equilibrium, examples for three traction separation laws are shown, for both homogeneous and inhomogeneous deformation. For a large range of values of the critical opening length the error scales almost linearly with this critical opening length. For large critical opening length the error may even become significant, requiring the use of a traction separation law that satisfies the condition for rotational equilibrium. [Copyright &y& Elsevier]

Abstract: The purpose of the current work is the development and application of a new experimental technique and testing device for investigating the complex behavior of sheet metals during non-proportional loading. The method is based on plain strain pure bending, enabling the investigation of large deformation cyclic reversed loading, orthogonal pure bending, as well as springback. The key feature of the pure bending experiment is the absence of contact forces, material slip and friction. Furthermore, during the pure bending test, the strain gradient through the thickness is kinematically prescribed because the specimen is subjected to a plane strain condition in de direction parallel to the rotational axis (), which allows for a straightforward comparison of the pure bending experiments and parallel simulations. The latter is used here via the identification of a recent model for directional hardening effects and arbitrary strain path changes, (). The current method facilitates experimental investigation of hardening stagnation after reverse loading and cross hardening going well beyond that which is possible with existing methods based on the cyclic shear or tension-shear of sheet metal strips (.), or pure and three-point bending (). [Copyright &y& Elsevier]

Abstract: In this paper, the delamination in pre-strained polymer coated steel is quantitatively characterized through a combined numerical–experimental approach. The surface roughening of the steel substrate is analyzed by a correlation technique and coupled to the pre-deformation of the coating. The polymer coating shows a clear stress relaxation after pre-deformation, which requires special attention for the correct numerical characterization of the interface. A large displacement cohesive zone model is extended with an interfacial pre-damage parameter representing the loss of adhesion due to substrate roughening. Finally, peel tests are performed on pre-strained specimens, on the basis of which the interface is characterized by an inverse parameter identification procedure. [Copyright &y& Elsevier]

Abstract: In ball grid array (BGA) packages, solder balls are exposed to cyclic thermo-mechanical strains arising from the thermal mismatch between package components. Thermo-mechanical fatigue crack propagation in solder balls is almost always observed at the chip side of the bump/pad junction. The objective of the experimental part of this study is to characterize the bump/pad interface under fatigue loading. Fatigue specimens are prepared by reflowing Sn3.8Ag0.5Cu lead-free solder alloy on Ni/Au substrates. Obtained results show that fatigue damage evolution strongly depends on the microstructure. Applied strain and solder volume both have an influence on the fatigue damage mechanism. In the numerical part of the study, fatigue experiments are modeled using the finite element technique. A cohesive zone approach is used to predict the fatigue damage evolution in soldered connections. Crack propagation is simulated by an irreversible linear traction–separation cohesive zone law accompanied by a non-linear damage parameter. Cohesive zone elements are placed where failure is experimentally observed. Damage evolution parameters for normal and tangential interaction are scrutinized through dedicated fatigue tests in pure tensile and shear directions. The proposed cohesive zone model is quantitatively capable of describing fatigue failure in soldered joints, which can be further extended to a numerical life-time prediction tool in microelectronic packages. [Copyright &y& Elsevier]

Abstract: A finite element analysis has been performed of the thermal cycling of Sn–Ag–Cu solder. Experimental observations revealed damage to occur at grain boundaries even in the absence of external mechanical loading. The effect of the anisotropy of the material has been investigated through a three-dimensional simulation of the experiment. Anisotropy was included in the model in the elastic and thermal expansion properties. Stress concentrations arise at grain boundaries, dependent on the orientation of the connected grains and their interface. Qualitative comparison of the numerical results with the experimental observations indicated a reasonable agreement. A more accurate prediction requires three-dimensional experimental data on the grain structure of the sample. [Copyright &y& Elsevier]

Abstract: Interfacial fibrilation is a typical mechanism that frequently occurs during delamination of a polymer coating from a steel substrate. It involves large displacements at the interface as well as large deformations in the bulk material. Classical small displacement cohesive zone formulations fail to describe such large deformations correctly. Therefore, a generic cohesive zone model is introduced that is suitable to describe both uniform and non-uniform fracture at an interface with large deformations in the delaminating bulk and large displacements at the crack tip. [Copyright &y& Elsevier]

Abstract: Delamination between a coating and a substrate is often an undesired phenomenon, for which predictive numerical schemes are required. The interface between the coating and the substrate is commonly described by cohesive zones, for which several different cohesive zone laws have been proposed in literature. Among the widening class of developed cohesive zone laws this paper focuses on the most frequently adopted law of Xu and Needleman. It is shown that this cohesive zone law needs improvement in order to describe a mixed-mode decohesion process. This conclusion is based on investigations of the influence of the coupling parameters and the assessment of the work-of-separation under mixed-mode conditions. Remedies for this problem with the Xu and Needleman law are not yet available in literature. An alternative exponential cohesive zone law, derived from the law of Xu and Needleman, is presented, which correctly describes mixed-mode decohesion. Attention is also given to the practical determination of all the parameters involved. [Copyright &y& Elsevier]

Abstract: This paper presents a numerical–experimental analysis of damage engineering applied to a well-known industrial problem. Many food cans are manually opened by raising a tab on the lid, thus initiating a crack, which is propagated along a circumferential groove. The influence of the groove geometry and depth on the opening force and the resistance against premature opening is investigated for some packaging materials, by making use of dedicated experimental techniques and an operator-split damage-plasticity framework. Attention is focused on a small part of the groove at a location halfway the circular crack-path, 900 from the crack initiation point. First, the groove manufacturing is analyzed by pressing a punch into a thin sheet of the material. Grooved specimens are loaded in tension, simulating the internal pressure during sterilization, and in shear, simulating the opening. Experiments have been carried out using a miniaturized tensile/compression stage located in the objective field of an optical microscope. For the computational analysis, an operator-split damage-plasticity model is proposed, where ductile damage is easily operated in conjunction with standard plasticity models. Simulations are done within a geometrically non-linear context, using a hypo-elasto-plastic material model with non-linear hardening and a contact algorithm to simulate the contact bodies in the groove forming process. An arbitrary–Lagrange–Euler (ALE) technique and adaptive remeshing are used to assure mesh quality during the large deformation process. The operator-split procedure used for the solution of the governing equations, allows to make easy use of a non-local damage operator as an extra feature within a commercial FEM package. Experimental results reveal that a reduction up to 20% for the opening force with unchanged pre-opening resistance can be reached with the use of an asymmetric punch for the groove forming. Numerical and experimental results are in good agreement. Simulations show that the industrial process of can lid production can be optimized considerably by controlling damage evolution in the first stage of the process. [Copyright &y& Elsevier]

Abstract: A phase field model is presented to describe the mechanical behaviour of microstructure dependent materials, which is demonstrated by applying it to eutectic tin–lead solder. This solder material is known to be heavily influenced by its continuously evolving microstructure. For the constitutive behaviour of the different phases the elasto-viscoplastic Perzyna model has been used. It is coupled to the phase field model through the constitutive parameters which are taken dependent on the mass fraction field resulting from the solution of the phase field equations. [Copyright &y& Elsevier]

The objective of this work is to model the fatigue damage process in a solder bump subjected to cyclic loading conditions. Fatigue damage is simulated using the cohesive zone methodology. Damage is assumed to occur at interfaces modeled through cohesive zones in the material, while the bulk material is assumed to be linear elastic. The state of damage at a cohesive zone is incorporated into the cohesive zone constitutive law by a elasticity-based damage variable. The gradual degradation of the solder material and the corresponding damage accumulation throughout the cycling process is accounted for by a damage evolution law which captures the main damage characteristics. The model prediction of the solder bump life-time is shown to be in good agreement with one of the commonly used empirical life-time prediction laws. [Copyright &y& Elsevier]

Fibrillating metal-elastomer interfacial systems, typically used in stretchable electronics applications, can exhibit remarkably high values for the interface fracture toughness. Consequently, a huge gap exists between the low adhesion energy at the microscopic scale and the measured macroscopic work of separation. This contribution aims to close this energy gap by unravelling the underlying dissipative mechanisms through a multi-scale approach. The first scale transition was established in earlier work, and concerned the formation and deformation of a single fibril at the copper-rubber interface up to failure. It was shown that the obtained work of separation was significantly larger than the small-scale interface adhesion, yet a decade too small with respect to the experimental values. In order to close the energy gap, in this contribution, the second scale transition is achieved by considering a finite number of elongating discrete hyperelastic fibrils within the fracture process zone. It is shown that the dynamic release of the stored elastic energy by fibril fracture that results from the spatial discreteness of multiple fibrils, the interaction with the adjacent deforming bulk elastomer material and the highly nonlinear behavior of the elastomer provides an explanation for the high work of separation values. In addition, an intrinsic shortcoming of cohesive zone formulations at the macroscopic scale is revealed. The results provide a mechanistic understanding of the physics involved with interface delamination through fibrillation in metal-elastomer interfaces. [ABSTRACT FROM AUTHOR]

High values for the work of separation have been reported in peel tests on fibrillating interfacial systems. The exact origin of these high values is not properly understood, since it remains unclear which dissipative mechanisms related to fibrillation cause a significant increase in the work of separation. In this paper, the contribution of fibril mechanics to the work of separation is quantified. To this end, a micromechanical model of a single fibril is used, in which the growth of a nucleated fibril up to the moment of fracture is described. The initial geometry is varied to reflect the variability in the substrate profile. It is observed that the stresses and strains that occur in the model are well beyond typical bulk values. Given the large variation in measured stress–strain curves for rubber materials reported in literature, a small scale single fibril experiment is performed to assess the applicability of reported bulk material parameters to this problem. The obtained experimental response falls well within the model bandwidth for the range of material parameters from literature. Furthermore, the fibril fracture stress, which serves as the failure criterion in the model, is extracted from the experiment. From the micromechanical model results, it appears that, for the considered range of material properties, the work of separation is mainly influenced by the fracture stress. Furthermore the initial geometry has a profound influence on the obtained work of separation. It is concluded that the work of separation determined from the micro-model is significantly larger than the intrinsic adhesion energy, yet it remains still an order of magnitude smaller than the values reported in literature. For the considered system this indicates that, although it has a significant contribution, fibril deformation is not the only contribution to the high work of separation. [ABSTRACT FROM AUTHOR]

A novel methodology is presented for pre-conditioning a polymer-coated steel used in food and beverage packaging. Mechanical rejuvenation of the coating via rolling is studied in order to prevent interface damage in subsequent forming operations. The simulations reveal that the thermodynamic state of the polymer coating after rolling depends on the rolling reduction. This dependency can be used to tailor the thermodynamic state of the coating prior to can production. A proof-of-principle simulation was performed to study the effects of rejuvenation on subsequent deformation processes. Deformation-induced interface roughening was studied for the initial and rejuvenated polymer coating. The predictions for a rejuvenated polymer coating indicate a significant decrease in interface damage. The presented numerical framework allows for a detailed study of the effects of pre-conditioning on the interface integrity during subsequent forming operations. With properly identified material parameters, it becomes possible to tailor the polymer–steel material properties before and during production to minimize interface damage during production and storage of cans or canisters, e.g. for food and beverage packaging. [ABSTRACT FROM AUTHOR]

The effect of collagen fibers on the mechanics and hemodynamics of a trileaflet aortic valve contained in a rigid aortic root is investigated in a numerical analysis of the systolic phase. Collagen fibers are known to reduce stresses in the leaflets during diastole, but their role during systole has not been investigated in detail yet. It is demonstrated that also during systole these fibers substantially reduce stresses in the leaflets and provide smoother opening and closing. Compared to isotropic leaflets, collagen reinforcement reduces the fluttering motion of the leaflets. Due to the exponential stress–strain behavior of collagen, the fibers have little influence on the initial phase of the valve opening, which occurs at low strains, and therefore have little impact on the transvalvular pressure drop. [Copyright &y& Elsevier]

Numerical analysis of the aortic valve has mainly been focused on the closing behaviour during the diastolic phase rather than the kinematic opening and closing behaviour during the systolic phase of the cardiac cycle. Moreover, the fluid–structure interaction in the aortic valve system is most frequently ignored in numerical modelling. The effect of this interaction on the valve''s behaviour during systolic functioning is investigated. The large differences in material properties of fluid and structure and the finite motion of the leaflets complicate blood–valve interaction modelling. This has impeded numerical analyses of valves operating under physiological conditions. A numerical method, known as the Lagrange multiplier based fictitious domain method, is used to describe the large leaflet motion within the computational fluid domain. This method is applied to a three-dimensional finite element model of a stented aortic valve. The model provides both the mechanical behaviour of the valve and the blood flow through it. Results show that during systole the leaflets of the stented valve appear to be moving with the fluid in an essentially kinematical process governed by the fluid motion. [Copyright &y& Elsevier]

A novel integrated framework is presented for the prediction of deformation-induced interface roughening and failure in polymer-coated steels. Crystal plasticity is employed to predict the change in steel surface roughness in-situ. The steel substrate is coated with a thin polymer layer and the polymer–steel interface is modeled using an exponential cohesive zone law. Uniaxial tensile simulations are performed and the results show that the predicted roughness increases with the applied deformation. The local changes in the steel surface profile result in initiation and growth of local interface failure. Furthermore, a compression simulation shows that the roughening rate of the steel is increased compared to tension, with an increase in the predicted interface damage as a result. The presented framework thus allows for a detailed numerical study of the initiation and growth of interface damage in polymer-coated steels during applied deformation. The incorporation of the crystal plasticity model to predict the changes in the steel surface profile complements the cumbersome measurements of detailed experimental displacement fields that accompany deformation-induced roughening and thus enables the analysis of deformation processes where measuring the steel surface profile is difficult if not impossible, e.g. industrial forming processes such as deep-drawing. [ABSTRACT FROM AUTHOR]

Abstract: A constitutive model is presented for predicting the stresses in thermosetting resins during and after cure. An overview is given of the experimental techniques used for estimating the parameters in this model. The model is validated by comparing its predictions to a second set of measurements that has not been used for the actual parameter estimation. This validation shows that the model is capable of giving fair predictions of the measured stresses. The model is implemented in a commercially available finite element package and its use is demonstrated by applying it to the study of a flip-chip underfilling process. [Copyright &y& Elsevier]

The importance of the aortic root compliance in the aortic valve performance has most frequently been ignored in computational valve modeling, although it has a significant contribution to the functionality of the valve. Aortic root aneurysm or (calcific) stiffening severely affects the aortic valve behavior and, consequently, the cardiovascular regulation. The compromised mechanical and hemodynamical performance of the valve are difficult to study both ‘in vivo’ and ‘in vitro’. Computational analysis of the valve enables a study on system responses that are difficult to obtain otherwise. In this paper a numerical model of a fiber-reinforced stentless aortic valve is presented. In the computational evaluation of its clinical functioning the interaction of the valve with the blood is essential. Hence, the blood–tissue interaction is incorporated in the model using a combined fictitious domain/arbitrary Lagrange–Euler formulation, which is integrated within the Galerkin finite element method. The model can serve as a diagnostic tool for clinical purposes and as a design tool for improving existing valve prostheses or developing new concepts. Structural mechanical and fluid dynamical aspects are analyzed during the systolic course of the cardiac cycle. Results show that aortic root compliance largely influences the valve opening and closing configurations. Stresses in the delicate parts of the leaflets are substantially reduced if fiber-reinforcement is applied and the aortic root is able to expand. [Copyright &y& Elsevier]