Fracture criterion for kinking cracks in a tri-material adhesively bonded joint under mixed mode loading

The fracture behavior of a composite/adhesive/steel bonded joint was investigated by using double cantilever beam specimens. A starter crack is embedded at the steel/adhesive interface by inserting Teflon tape. The composite adherend is a random carbon fiber reinforced vinyl ester resin composite while the other adherend is cold rolled steel. The adhesive is a one-part epoxy that is heat cured. The Fernlund-Spelt mixed mode loading fixture was employed to generate five different mode mixities. Due to the dissimilar adherends, crack turning into the adhesive (or crack kinking) associated with joint failure, was observed. The bulk fracture toughness of the adhesive was measured separately by using standard compact tension specimens. The strain energy release rates for kinking cracks at the critical loads were calculated by a commercial finite element analysis software ABAQUS in conjunction with the virtual crack closure technique. Two fracture criteria related to strain energy release rates were examined. These are (1) maximum energy release rate criterion (G_max) and, (2) mode I facture criterion (G_II = 0). They are shown to be equivalent in this study. That is, crack kinking takes place at the angle close to maximum G or G_I (also minimum G_II, with a value that is approximately zero). The average value of G_IC obtained from bulk adhesive tests using compact tension specimens is shown to be an accurate indicator of the mode I fracture toughness of the kinking cracks within the adhesive layer. It is concluded that the crack in tri-material adhesively bonded joint tends to initiate into the adhesive along a path that promotes failure in pure mode I, locally.     

Crack deflection at an interface of alumina/metal joint: A numerical analysis

Deflection of a crack at the bimaterial interface is the initial mechanism required for obtaining enhanced toughness in bimaterial system. In this paper, a criterion is presented to predict the competition between crack deflection and penetration at the interface, using an energy release rate criterion. The finite element methods are used to calculate the strain energy release rates at the crack tip of alumina–metal bimaterial that either deflect or penetrate at the interface as a function of elastic mismatch and length of the deflected or penetrated crack. The effects of the elastic properties of two bonded materials were highlighted in order to evaluate the conditions for the crack deflection by the interface as well as the distance between the crack tip and the interface.     

Mixed Mode I/II fatigue crack growth in adhesive joints

Fatigue crack growth (FCG) tests have been carried out on adhesively bonded compact tension-shear (CTS) specimens to assess the behaviour of a structural adhesive under Mixed Mode I/II conditions. The fractographic analysis revealed that energy dissipation mechanisms due to inelastic phenomena like bulk plastic deformation and crazing are more pronounced in Mode I than in Mixed Mode and Mode II. This is reflected by a FCG rate that increases going from Mode I to Mode II for a given value of the range of strain energy release rate, ΔG.     

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.     

Some comments on the Arcan mixed-mode (I/II) test specimen

Although the Arcan specimen has been used frequently for mixed-mode crack growth testing using single-axis servohydraulic test equipment, the specimen and its commonly-used fixturing have features and behaviors that have implications to the proper understanding of results garnered from their use. These implications extend to hardware issues as well, as the Arcan specimen (when mounted at off-axis angles) can generate significant and even potentially damaging side loads on the load frame actuator. This paper discusses a number of the issues associated with the Arcan specimen and Arcan testing.     

Crack growth retardation following the application of an overload cycle using a strip-yield model

Experiments have shown that the application of an overload cycle can act to retard crack growth and even potentially lead to crack arrest. This paper describes a new method for investigating fatigue crack growth after the application of an overload cycle under plane stress conditions. The developed method is based on the concept of plasticity-induced crack closure and utilises the distributed dislocation technique and a modified strip-yield model. The present results are compared to previous experimental data for several materials. A good agreement is found, with the predictions showing the same trends in the various stages of post-overload crack growth.     

Modeling of facesheet crack growth in titanium-graphite hybrid laminates. Part II: Experimental results

Titanium-graphite hybrid composite laminates exhibit a coupled damage growth mode of facesheet cracking and delamination. Part I of this work modeled the growth of the coupled damage mode. Fatigue experiments were conducted on single edge notch tension specimens to measure the crack growth rate. This paper compares the model predictions with experimental data. The three-dimensional finite element model successfully captured the damage growth behavior for two of the lay-ups ([Ti/0/90/0₂]_s and [Ti/90/0/90₂]_s) in the experimental program. However, in a third lay-up, [Ti/0/90/±30]_s, the underlying damage modes were found to be sufficiently different than the other two lay-ups and the model did not capture the steady-state growth behavior. The effects of temperature and specimen size were also investigated for TiGr laminates. Except for the effects of the load ratio, elevated temperatures did not affect the crack growth rate significantly. For wider specimens, the steady-state fatigue crack growth behavior was similar to the narrow specimens, indicating that the steady-state facesheet crack growth behavior is independent of specimen size.     

Mode I fatigue crack growth reduction mechanisms after a single Mode II load cycle

A single Mode II load cycle, large enough to create residual displacements, decreases the subsequent Mode I crack growth rate. The distance for Mode I crack growth rate to fully recover, i.e., revert to the same da/dN as before Mode II load, is much longer than Mode II plastic zone size. The higher Mode II load, the larger is the reduction in growth rate and the longer the recovery distance. Higher Mode I R-ratio means smaller reduction in growth rate. Above a certain R-ratio, no reduction occurs at all. In the present study it is found that the reduction in growth rate is solely caused by crack closure due to tangential displacement of crack-surface irregularities that induce a surface mismatch between the upper and lower crack faces. The mechanism is called Mode II-induced crack closure. A model based on both analytical and experimental results is developed in order to estimate the degree of Mode II-induced crack closure after a Mode II load.     

Modeling of facesheet crack growth in titanium-graphite hybrid laminates, Part I

Experimental observations have indicated that in titanium-graphite hybrid laminates, fatigue cracks in the titanium facesheets initiate at free edges as well as in areas of high stress concentration, such as holes and notches. In addition, a delaminated region between the facesheet and the intact plies develops and propagates in the wake of the facesheet crack. This paper investigates different modeling techniques for predicting the coupled damage growth. Two modeling approaches were applied; a two-dimensional bridged-crack (BC) model and the virtual crack closure technique (VCCT). The VCCT was applied in two and three-dimensional finite element models and the trends were shown to be the same for both cases. However, the trends predicted using the VCCT are significantly different than the BC model. The reasons for the discrepancies are discussed. The model predictions are compared to experimental results in the second part of this paper.     

Obtaining mode mixity for a bimaterial interface crack using the virtual crack closure technique

We review, unify and extend work pertaining to evaluating mode mixity of interfacial fracture utilizing the virtual crack closure technique (VCCT). From the VCCT, components of the strain energy release rate (SERR) are obtained using the forces and displacements near the crack tip corresponding to the opening and sliding contributions. Unfortunately, these components depend on the crack extension size, Δ, used in the VCCT. It follows that a mode mixity based upon these components also will depend on the crack extension size. However, the components of the strain energy release rate can be used for determining the complex stress intensity factors (SIFs) and the associated mode mixity. In this study, we show that several—seemingly different—suggested methods presented in the literature used to obtain mode mixity based on the stress intensity factors are indeed identical. We also present an alternative, simpler quadratic equation to this end. Moreover, a Δ-independent strain energy release based mode mixity can be defined by introducing a “normalizing length parameter.” We show that when the reference length (used for the SIF-based mode mixity) and the normalizing length (used for Δ-independent SERR-based mode mixity) are equal, the two mode mixities are only shifted by a phase angle, depending on the bimaterial parameter ε.     

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.     

Interlaminar crack onset in co‐cured and co‐bonded composite joints under mode I cyclic loading

Composite joints exhibit different behavior in regard to delamination resistance when dealing with fatigue phenomenon. This research work focuses on an investigation to understand the failure mechanisms on the interfacial strength domain for delamination onset in cocured and cobonded joints. The analysis was based on strain energy release rate versus number of cycles plots that were obtained from fatigue tests in mode I with a stress ratio R = 0.1. The analysis encompassed from the microscopic to mesoscopic level obtained from scanning electron microscopic, and the images processed to extract the most relevant fracture patterns. The main difference between the two technologies was the stress concentration at the crack tip in which the cobonded joint presents a fabric carrier that blunts the adhesive layer, then delaying the delamination. This paper provides important information and guidelines to aid designers in the selection of the best composite joint for high‐performance structural applications.     

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.     

Predicting fatigue crack growth rate in a welded butt joint: The role of effective R ratio in accounting for residual stress effect

A simple and efficient method is presented in this paper for predicting fatigue crack growth rate in welded butt joints. Three well-known empirical crack growth laws are employed using the material constants that were obtained from the base material coupon tests. Based on the superposition rule of the linear elastic fracture mechanics, welding residual stress effect is accounted for by replacing the nominal stress ratio (R) in the empirical laws by the effective stress intensity factor ratio (R_eff). The key part of the analysis process is to calculate the stress intensity factor due to the initial residual stress field and also the stress relaxation and redistribution due to crack growth. The finite element method in conjunction with the modified virtual crack closure technique was used for this analysis. Fatigue crack growth rates were then calculated by the empirical laws and comparisons were made among these predictions as well as against published experimental tests, which were conducted under either constant amplitude load or constant stress intensity factor range. Test samples were M(T) geometry made of aluminium alloy 2024-T351 with a longitudinal weld by the variable polarity plasma arc welding process. Good agreement was achieved.     

Strain energy release rate calculation for a moving delamination front of arbitrary shape based on the virtual crack closure technique. Part I: Formulation and validation

This paper proposes a simple, efficient algorithm to trace a moving delamination front with an arbitrary and changing shape so that delamination growth can be analyzed by using stationary meshes. Based on the algorithm, a delamination front can be defined by two vectors that pass through any point on the front. The normal vector and the tangent vector for the local coordinate system can then be obtained based on the two delamination front vectors. An important feature of this approach is that it does not require the use of meshes that are orthogonal to the delaminations front. Therefore, the approach avoids adaptive re-meshing techniques that may create a large computational burden in delamination growth analysis. An interface element that can trace the instantaneous delamination front, determine the local coordinate system, approximate strain energy release rate components and apply fracture mechanics criteria has been developed and implemented into ABAQUS^® with its user-defined element (UEL) feature. In this Part I of a two-part paper, the approach and its implementation are described and validated by comparison to results from existing cases having analytical solutions or other established FEA predictions.     

Strain energy release rate calculation for a moving delamination front of arbitrary shape based on the virtual crack closure technique. Part II: Sensitivity study on modeling details

The interface element and VCCT process described in Part I of this two-part paper, developed to compute strain energy release rates of an arbitrary delamination front using non-orthogonal finite element meshes, are further investigated in this paper for robustness and ease of use in tracking delamination growth. Standard 3-D elements are used in conjunction with the interface elements. No special singularity elements are required. Stationary meshes that are independent of the shape of the delamination front can be used. Three cases having different initial delamination shapes are examined. The process is shown to be insensitive to the values used for the interfacial spring stiffness, the orientation of the interface element, or even the mesh pattern if the mesh has a reasonable degree of refinement. Therefore, the method can be used with ease and confidence in general-purpose delamination growth analysis for engineering applications.     

Probabilistic fatigue crack growth analysis of spot‐welded joints

This paper presents a probabilistic fatigue crack growth life prediction methodology for spot‐welded joints under variable amplitude loading history. The loading is multi‐axial and is obtained from transient response analysis of a vehicle model using finite‐element analysis. A three‐dimensional (3D) finite element model of a simplified joint with four spot welds is developed, and the static stress analysis of this joint is performed. Then the fatigue crack inside the base material sheet is modelled as a surface crack. Probabilistic crack growth model is combined with the stress analysis result to develop a probabilistic fatigue crack growth life prediction methodology for spot welds. This new method is implemented with MSC/NASTRAN and MSC/FATIGUE and is useful for the reliability assessment of spot‐welded joints against fatigue crack growth.     

Fatigue growth behavior for surface crack in welding joints under combined compressive and bending stresses

It has been demonstrated by experiments that crack can grow under cyclic compressive loading. However, it is difficult to observe and describe accurately by mathematical methods. In addition, cracks may close under compressive loading, which also increases the complexity of the problem. The fatigue growth behavior for surface cracks under biaxial loadings was studied by fatigue tests of HTS-A steel. According to experimental evidences, it is concluded that the transverse compressive stress not only changes the fracture morphology but also affect crack propagation life. Considering the influence of the compressive stress, this paper proposed an equivalent SIF and crack growth model subjected to compressive and bending stresses on the basis of McEvily formula. Finally, comparisons are made between prediction results and experimental data.     

Role of plastic zone in crack growth direction criterion under mixed mode loading

An approach to determine the crack growth direction under mixed-mode loading conditions is presented. The plastic zone shape around the crack tip is applied for evaluating angle of crack propagation. It is proposed that a mixed-mode crack will extend along the plastic zone radius with a minimum value. The prediction of the proposed criterion is compared with the experimental data and other models. The agreement is fairly good.