Experimental and numerical investigations of mixed mode crack growth resistance of a ductile adhesive joint

Polymeric adhesive joints are extensively employed in various industrial and technological applications. It has been observed that in ductile adhesive joints, interface fracture is a common mode of failure which may involve stable crack propagation followed by catastrophic growth. The objectives of this paper are to investigate the effects of bondline thickness and mode mixity on the steady state energy release rate J_ss of such a joint. To this end, a combined experimental and numerical investigation of interfacial crack growth is carried out using a modified compact tension shear specimen involving two aluminium plates bonded by a thin ductile adhesive layer. A cohesive zone model along with a simple traction versus separation law is employed in the finite element simulations of crack growth. It is observed that J_ss increases strongly as mode II loading is approached. Also, it enhances with bondline thickness in the above limit. These trends are rationalized by examining the plastic zones obtained from the numerical simulations. The numerically generated J_ss values are found to agree well with the corresponding experimental results.     

Influence of crack tip constraint on void growth in pressure sensitive plastic solids - I: 2D analysis

In this work, the effect of constraint on void growth near a notch tip under mode-I loading is investigated in materials exhibiting pressure sensitive yielding and plastic dilatancy. To this end, large deformation elastic-plastic finite element analyses are performed using a two-dimensional (2D) plane strain, modified boundary layer formulation by prescribing the elastic K − T field as remote boundary conditions. The analyses are conducted for different values of K (or J) and T-stress. The material is assumed to obey a finite strain, Extended Drucker-Prager yield condition. The roles of pressure sensitivity, plastic dilatancy and yield locus shape on the interaction between the notch and a nearby void are studied by examining the distribution of hydrostatic stress and plastic strain in the ligament connecting them as well as the growth of notch and the void. The results show that void growth with respect to J is enhanced due to pressure sensitivity, and more so when the plastic flow is non-dilatational. By contrast, irrespective of pressure sensitivity, loss of crack tip constraint can significantly retard void growth.     

Investigation of crack tunneling in ductile materials

Crack tunneling has been commonly observed in crack growth experiments on specimens made of ductile materials such as steel and aluminum alloys. The objective of this study is to investigate the crack tunneling phenomenon and study the effects of crack tunneling on the distribution of several mechanics parameters controlling ductile fracture. Three-dimensional (3D) elastic-plastic finite element analyses of stable tearing experiments involving tunneling fracture are carried out. Two model problems based on stable tearing experiments are considered. The first model problem involves a plate specimen containing a stationary, single-edge crack with a straight or tunneled crack front, under remote mode I loading. In the numerical analyses, the crack tip opening displacement, the von Mises effective stress, the mean stress, the stress constraint and the effective plastic strain around straight and tunneled crack fronts are obtained and compared. It is found that crack tunneling produces significant changes in the stress and deformation fields around the crack front. The second model problem involves a specimen containing a stably growing single-edge crack with a straight or tunneled crack front, under remote mode I loading. Crack growth events with a straight or tunneled crack front are simulated using the finite element method, and the effect of crack tunneling on the prediction of the load-crack-extension response based on a CTOD fracture criterion is investigated.     

Fatigue crack closure determination by means of finite element analysis

Plasticity-induced crack closure is an observed phenomenon during fatigue crack growth. However, accurate determination of fatigue crack closure has been a complex task for years. It has been approached by means of experimental and numerical methods. The finite element method (FEM) has been the principal numerical tool employed. In this paper the results of a broad study of fatigue crack closure in plane stress and plane strain by means of FEM are presented. The effect of three principal factors has been analysed in depth, the maximum load, the crack length and the stress ratio. It has been found that the results are independent of maximum load and the crack length, and there exists a direct influence of the stress ratio. This relation has been numerically correlated and compared with experimental results. Differences have also been established between opening and closure points and between the different criteria employed to compute crack closure.     

Influence of minimum element size to determine crack closure stress by the finite element method

Measuring opening or closure stress is a complex process that influences the low accuracy of obtained data. Finite element models have been one of the available ways to deal with this problem. The difficulty of modelling the whole process of crack growth (due to the great number of cycles implied) as the great complexity of the phenomenon itself (with a high plastic strain concentrated in a small area, with elevated stress gradients) has made the results to be quite varied, being influenced by a great number of modelling parameters. Of those parameters, the minimum size of the element used to mesh the area around the crack tip vicinity presents a great influence on the results.In this work, a detailed analysis of the influence of this parameter in the results in terms of closure or opening stress is presented. The effect that different meshing criteria can have on the result is complex and it has been necessary to reduce the element size around the crack tip to a size that had not been reached before. Procedures and modelling criteria stricter than the ones shown in the current bibliography are proposed. A methodology for the correct interpretation of the results is also established.     

A finite element ductile failure simulation method using stress-modified fracture strain model

This paper proposes a new method to simulate ductile failure using finite element analysis based on the stress-modified fracture strain model. A procedure is given to determine the stress-modified fracture strain as a function of the stress triaxiality from smooth and notched bar tensile tests with FE analyses. For validation, simulated results using the proposed method are compared with experimental data for cracked bar (tensile and bend) tests, extracted from API X65 pipes, and for full-scale burst test of gouged pipes, showing overall good agreements. Advantages in the use of the proposed method for practical structural integrity assessment are discussed.     

Three-dimensional finite element simulations of mixed-mode stable tearing crack growth experiments

Mixed-mode stable tearing crack growth events in Arcan plate specimens made of aluminum alloy 2024-T3 are simulated using three-dimensional (3D) finite element methods. A modeling/simulation procedure utilizing a mixed-mode CTOD fracture criterion and the custom 3D crack growth simulation software, CRACK3D, with an automatic local re-meshing option is demonstrated. Simulation predictions of the load-crack extension curve and the in-plane curvilinear crack growth path are compared with experimental measurements for various mixed-mode loading cases. Issues such as the effects of near-tip finite element size and crack extension increment size on simulation predictions are investigated.     

Elasto-plastic finite element analysis of a crack in an infinite plate

The elastic support method was recently developed to simulate the effects of unbounded solids in the finite element analysis of stresses and displacements. The method eliminates all the computational disadvantages encountered in the use of `infinite' elements or coupled finite element boundary element methods while retaining all the computational advantages of the finite element method. In this paper, the method is extended to the elasto-plastic analysis of fracture in infinite solids by using the load increment approach and including the effects of strain hardening. Numerical tests and parametric study are conducted by analysing a straight crack in an infinite plate. Present results for J integrals and plastified zones are compared, respectively, with analytical solutions and available results obtained by using the body force method. The agreement between the results is found to be very good even if the truncation boundary of the finite element model is located very close to the crack tip or the plastified zone.     

Numerical characterisation of the fibre-matrix interface crack growth in composites under transverse compression

Inter-fibre failure under compression transverse to the fibres is studied at micromechanical level. Interfacial fracture mechanics concepts, associated to both the open model and the contact model, are applied. A numerical study is performed using the boundary element method aimed at explaining the origin and evolution of the damage at micromechanical level, considered as fibre-matrix interface cracks. Assuming that the damage starts as small debonds originated by shear stresses at the position where their maximum values are reached, it has been found that the crack shows different morphologies at both tips: an open one and a closed one with a large contact zone. Then the interface crack grows unstably in mixed mode only on the open tip side until this growth changes to stable, once the crack closes at this tip, with the generation of a contact zone.     

Constraint effects on multiple void interaction in pressure sensitive plastic solids

In this work, effects of pressure sensitive yielding and plastic dilatancy on void growth and void interaction mechanisms in fracture specimens displaying high and low constraint levels are investigated. To this end, large deformation finite element simulations are carried out with discrete voids ahead of the notch. It is observed that multiple void interaction mechanism which is favored by high initial porosity is further accelerated by pressure sensitive yielding, but is retarded by loss of constraint. The resistance curves predicted based on a simple void coalescence criterion show enhancement in fracture resistance when constraint level is low and when pressure sensitivity is suppressed.     

Damage mechanics models of ductile crack growth in welded specimens

Two-dimensional, plane strain, finite element analyses of strength-mismatched welded joints have been performed using the modified boundary layer formulation. The welds were idealized as two-material joints with the material interface running parallel to the crack, which was embedded in the weld material. The Rousselier ductile damage model was employed within the weld material to simulate crack extension due to the growth and coalescence of microvoids. By analysing models with different levels of material mismatching, weld dimensions and applied T -stress levels, it was possible to analyse the effects of crack tip constraint due to both material mismatching and specimen geometry on the fracture resistance of the weld material.
The results show that material strength overmatching (where the weld material is stronger than the base material) reduces the level of constraint ahead of the crack, which can increase the resistance to fracture of the weld material. Conversely, material strength undermatching increases crack tip constraint, reducing the fracture resistance of the joint. By employing estimates for the crack tip constraint levels, Q _M , based on the applied load, level of material mismatching and weld region thickness, it has been possible to 'order' the J– resistance curves of overmatched joints by generating a family of J–Q _M loci which describe the effects of constraint on the fracture resistance of the weld material. However, it is shown that the Q _M-stress parameter is not capable of describing the effect of material strength undermatching on the fracture resistance of a joint, which can be much lower than that obtained from a high-constraint homogeneous specimen of weld material.     

Three-dimensional, parallel, finite element simulation of fatigue crack growth in a spiral bevel pinion gear

This paper summarizes new results for predicting crack shape and fatigue life for a spiral bevel pinion gear using computational fracture mechanics. The predictions are based on linear elastic fracture mechanics theories combined with the finite element method, and incorporating plasticity-induced fatigue crack closure and moving loads. We show that we can simulate arbitrarily shaped fatigue crack growth in a spiral bevel gear more efficiently and with much higher resolution than with a previous boundary-element-based approach [Spievak LE, Wawrzynek PA, Ingraffea AR, Lewicki DG. Simulating fatigue crack growth in spiral bevel gears. Engng Fract Mech 2001;68(1):53-76] using the finite element method along with a better representation of moving loads. Another very significant improvement is the decrease in solution time of the problem by employing a parallel PC-cluster, an approach that is becoming more common in both research and practice. This reduces the computation time for a complete simulation from days to a few hours. Finally, the effect of change in the flexibility of the cracking tooth on the location and magnitude of the contact loads and also on stress intensity factors and fatigue life is investigated.     

A study of crack growth retardation due to artificially induced crack surface contact

The contact of the cracked surfaces during a part of a loading cycle generally results in a reduced crack growth rate. A critical experiment was designed to evaluate the influence of the crack surface contact on crack growth. A round compact specimen made of 1070 steel with a round hole at the wake of the fatigue crack was designed. Two mating wedges were inserted into the hole of the specimen while the external load was kept at its maximum in a loading cycle. In this way, the wedges and the hole in the specimen were in firm contact during the entire loading cycle in the subsequent loading. Experiments showed that the addition of the wedges resulted in a reduction of crack growth rate in the subsequent constant amplitude loading. However, crack growth did not arrest. With the increase in the subsequent loading cycles, crack growth rate increased. The traditional crack closure concept cannot explain the experimental phenomenon because the effective stress intensity factor range was zero after the insertion of the wedges. The detailed stress–strain responses of the material near the crack tip were analyzed by using the finite element method with the implementation of a robust cyclic plasticity theory. A multiaxial fatigue criterion was used to determine the fatigue damage based upon the detailed stresses and strains. The crack growth was simulated and the predicted results were in good agreement with the experimental observations. It was confirmed that the stresses and strains near the crack tip governed cracking behavior. Crack surface contact reduced the crack tip cyclic plasticity and the result was the observed retardation in crack growth.     

Fracture of a ductile layer constrained by stiff substrates

A combined experimental and theoretical analysis of the fracture behaviour of brass/solder/brass sandwich specimens is conducted. First, the theories of interfacial fracture initiation for a ductile layer sandwiched between elastic substrates are reviewed. The fracture behaviours are then reported of brass/solder/brass sandwich specimens under various mode mixities. Additionally, the effects of solder layer thickness h and specimen lateral thickness t are presented. The effects of mode mix and plastic constraint on the failure mechanism and toughness are analysed.     

Vapor pressure assisted crack growth at interfaces under mixed mode loading

Moisture diffuses into the numerous pores and cavities formed in polymeric molding compounds, at the filler particle–polymer matrix interfaces and at polymer–silicon interfaces of IC packages. During reflow soldering, the rapidly expanding moisture generates high internal pressures within the voids which are comparable to yield strengths of the molding compounds at glass transition temperatures. The combined action of thermal stresses and high vapor pressure accelerates void growth, and ultimately leads to interface delamination and package cracking. In this study, the molding compound is taken to be an elastic–plastic material while the silicon substrate is treated as an elastic material. The extended Gurson model which incorporates vapor pressure as an internal variable is used to characterize the void growth and coalescence process at the interface. When the mode II loading is dominant, high vapor pressure can cause several-fold reduction in the interface fracture toughness.     

Elastic–plastic finite element analysis of the effect of compressive loading on crack tip parameters and its impact on fatigue crack propagation rate

The effects of applied compressive stress on the crack tip parameters and their implications on fatigue crack growth have been studied. Four center-cracked panel specimens with different crack lengths are analysed using finite element method. The results show that under tension–compression loading the local crack tip parameters are determined by two loading parameters. The two loading parameters are the maximum stress intensity and the maximum compressive stress in the applied stress cycle. Predictions of fatigue crack propagation behaviour based on the maximum stress intensity and maximum compressive stress agree well with experimental observations.     

Cohesive zone simulations of crack growth along a rough interface between two elastic-plastic solids

It has been known for many years that crack propagation along interfaces is influenced by interface topography or roughness profile. This has given rise to a small body of literature in which interface toughening with stochastic surface finishes, produced by grinding, rolling, or grit blasting, has been the primary focus. However, there is very little information currently available on the effect of patterned interfaces that are characterized by a minimal number of geometric parameters. In the present article, roughness-enhanced toughening of a cohesive interface between two identical materials is explored with a pure sinusoidal interface morphology that is characterized by its aspect ratio or ratio of amplitude to wavelength. Sixteen finite element meshes, each with a different aspect ratio, were constructed to study initiation and growth of a semi-infinite interface crack due to remote mode-I loading. The cohesive interface was modeled with a viscosity-modified Xu-Needleman cohesive zone law, and the solids were characterized with continuum elastic and elastic-plastic constitutive models. Predicted relationships between the aspect ratio and the macroscopic toughness point to key differences in the material models. A set of critical parameters which include the aspect ratio, material and cohesive properties is predicted such that catastrophic crack growth is inhibited due to crack blunting. A clear boundary between brittle and ductile fracture behavior is thus identified. The results suggest some guidelines for practical design of failure resistant interfaces through appropriate choice of geometric, material, and cohesive parameters.     

An embedded cohesive crack model for finite element analysis of brickwork masonry fracture

This paper presents a numerical procedure for fracture of brickwork masonry based on the strong discontinuity approach. The model is an extension of the cohesive model prepared by the authors for concrete, and takes into account the anisotropy of the material. A simple central-force model is used for the stress versus crack opening curve. The additional degrees of freedom defining the crack opening are determined at the crack level, thus avoiding the need of performing a static condensation at the element level. The need for a tracking algorithm is avoided by using a consistent procedure for the selection of the separated nodes. Such a model is then implemented into a commercial code by means of a user subroutine, consequently being contrasted with experimental results. Fracture properties of masonry are independently measured for two directions on the composed masonry, and then input in the numerical model. This numerical procedure accurately predicts the experimental mixed-mode fracture records for different orientations of the brick layers on masonry panels.     

Comparison of cohesive zone model and linear elastic fracture mechanics for a mode I crack near a compliant/stiff interface

Cohesive zone model has been widely applied to simulate crack growth along interfaces, but its application to crack growth perpendicularly across the interface is rare. In this paper, the cohesive zone model is applied to a crack perpendicularly approaching a compliant/stiff interface in a layered material model. One aim is to understand the differences between the cohesive zone model and linear elastic fracture mechanics in simulating mode I crack growth near a compliant/stiff interface. Another aim is to understand the effects of elastic modulus mismatch and cohesive strength of the stiff layer on the crack behavior near the interface. To simulate crack growth approaching an interface, the cohesive zone model which incorporates both the energy criterion and the strength criterion is an effective method.     

Variable amplitude crack growth in notched specimens

Predictions of variable amplitude fatigue crack growth in notched tensile specimens at an elevated temperature and relative high loads were conducted. The predictions were based on constant amplitude fatigue data and mean crack growth rates were calculated. Crack closure levels were calculated by comparison of crack closure free experimental data obtained with the so called constant K_I,max-method and nominal data. Also, numerical simulations of the closure level throughout the specimens were performed. Although experimental data showed rather large a scatter it was concluded that variable amplitude crack growth rates can be predicted with reasonable agreement using constant amplitude fatigue data. Also, crack growth rates cannot be predicted by LEFM in the inelastic notch affected zone, even if absence of crack closure is assumed.