Traction-separation Relation Research Articles

Encyclopedia of catalysis

Lattice trapping is an important aspect in accurately understanding the fracture behaviors of nanomaterials. Employing molecular dynamics simulations, we studied the lattice trapping of nanocracks in both single-crystal and polycrystalline graphene. Different crack-dislocation and crack-grain boundary configurations were constructed and investigated. It is found that cracks in single-crystal graphene exhibit negligible lattice trapping, with or without the presence of dislocations. On the other hand, lattice trapping in polycrystalline graphene may vary greatly and is shown to be directly correlated to the tensile strength of grain boundary. Moreover, we showed that unique dislocation-independent traction-separation behaviors, which are not affected by the presence of dislocations, exist for cracks in single-crystal graphene. The traction-separation relation was then fitted to a cohesive zone model to demonstrate the possibility of bridging atomistic modeling with large-scale numerical simulations. Our findings provide critical hints for atomistic-informed multiscale modeling of fracture of two-dimensional materials.

Ductile tearing in thin aluminum panels: experiments and analyses using large-displacement, 3-D surface cohesive elements

This paper describes a large-displacement formulation for a 3-D, interface-cohesive finite element model and its application to predict ductile tearing in thin aluminum panels. A nonlinear traction–separation relationship defines the constitutive response of the initially zero thickness interface elements. Applications of the model simulate crack extension in C(T) and M(T) panels made of a 2.3 mm thick, Al 2024-T3 alloy tested as part of the NASA-Langley Aging Aircraft program. Tests of the M(T) specimens without guide plates exhibit significant out-of-plane (buckling) displacements during crack growth which necessitates the large-displacement, cohesive formulation. The measured load vs. outside surface crack extension behavior of high constraint ( T-stress>0) C(T) specimen drives the calibration process of the cohesive fracture model. Analyses of low constraint M(T) specimens, having widths of 300 and 600 mm and various a/ W ratios, demonstrate the capabilities of the calibrated model to predict measured loads and measured outside surface crack extensions. The models capture accurately the strong 3-D effects leading to out-of-plane buckling and various degrees of crack front tunneling in the C(T) and M(T) specimens. Previous analyses of these specimens using a crack tip opening angle (CTOA) criterion for growth show good agreement with measured peak loads. However, without the ability of the interface-cohesive model to predict tunneling behavior, the CTOA approach overestimates crack extensions early in the loading when tunneling behavior dominates the response.

Crack growth predictions by cohesive zone model for ductile fracture

For crack growth by a ductile failure mechanism, the fracture process zone is represented in terms of special interface elements in the crack plane ahead of the crack. A porous ductile material model is used in the interface elements to represent the growth of voids to coalescence. In relation to the finite element mesh, the initial width of the interface is taken to be zero, but the traction separation relations represented by the interface are based on assuming an interface width of the order of the void spacing. The tangential stresses inside the interface are determined by the requirement of compatibility with the surrounding material in the tangential direction. Some comparison with predictions based on related crack growth models is used to discuss the performance of the special cohesive zone model presented here.

Simulation of ductile crack growth in thin aluminum panels using 3-D surface cohesive elements

This work describes the formulation and application of a 3-D, interface-cohesive finite element model to predict quasi-static, ductile crack extension in thin aluminum panels for mode I loading and growth. The fracture model comprises an initially zero thickness, interface element with constitutive response described by a nonlinear traction-separation relationship. Conventional volumetric finite elements model the nonlinear (elastic-plastic) response of background (bulk) material. The interface-cohesive elements undergo gradual decohesion between faces of the volumetric elements to create new traction free crack faces. The paper describes applications of the computational model to simulate crack extension in C(T) and M(T) panels made of a 2.3 mm thick, Al 2024-T3 alloy tested as part of the NASA-Langley Aging Aircraft program. Parameters of the cohesive fracture model (peak opening traction and local work of separation) are calibrated using measured load vs. outside surface crack extensions of high constraint (T-stress > 0) C(T) specimens. Analyses of low constraint M(T) specimens, having widths of 300 and 600 mm and various a/W ratios, demonstrate the capabilities of the calibrated model to predict measured loads and outside surface crack extensions. The models capture accurately the strong 3-D effects leading to various degrees of crack front tunneling in the C(T) and M(T) specimens. The predicted crack growth response shows rapid convergence with through-thickness mesh refinement. Adaptive load increment procedures to control the rate of decohesion in the interface elements leads to stable, rapidly converging iterations in the globally implicit solution procedures.

Analysis of the Symmetrical 90°-peel Test with Extensive Plastic Deformation

A numerical 2-D study of the symmetrical 90°-peel test (a similar geometry to the T-peel test) in which extensive plastic deformation occurs in the adherends is presented in this paper. A traction-separation relation is used to simulate failure of the interface, and the conditions for both crack initiation and steady-state crack growth are investigated. The numerical predictions for the steady-state peel force are compared with those based on elementary beam theory. It is shown that two competing effects dominate the mechanics of the peel test to such an extent that the results of beam-bending analyses cannot be used to predict the peel force. At one extreme range of parameters, delamination is driven by shear rather than by bending, resulting in a lower peel force than would be predicted by beam-bending analyses. At the other extreme, where delamination is bending-dominated, the constraint induced by the interfacial tractions cause an increase in the peel force. The numerical results are compared with the results of experiments in which adhesively-bonded specimens are tested in the symmetrical 90°-peel configuration. Excellent agreement between the numerical and experimental results validates the numerical approach.

Steady-state crack growth and work of fracture for solids characterized by strain gradient plasticity

Mode I steady-state crack growth is analysed under plane strain conditions in small scale yielding. The elastic-plastic solid is characterized by a generalization of J 2 flow theory which accounts for the influence of the gradients of plastic strains on hardening. The constitutive model involves one new parameter, a material length l, specifying the scale of nonuniform deformation at which hardening elevation owing to strain gradients becomes important. Gradients of plastic strain at a sharp crack tip result in a substantial increase in tractions ahead of the tip. This has important consequences for crack growth in materials that fail by decohesion or cleavage at the atomic scale. The new constitutive law is used in conjunction with a model which represents the fracture process by an embedded traction-separation relation applied on the plane ahead of the crack tip. The ratio of the macroscopic work of fracture to the work of the fracture process is calculated as a function of the parameters characterizing the fracture process and the solid, with particular emphasis on the role of l.