Constraint effects in adhesive joint fracture

Constraint effects in adhesive joint fracture are investigated by modelling the adherents as well as a finite thickness adhesive layer in which a single row of cohesive zone elements representing the fracture process is embedded. Both the adhesive and the adherents are elastic-plastic with strain hardening. The bond toughness Γ (work per unit area) is equal to Γ₀+Γ_p, where Γ₀ is the intrinsic work of fracture associated with the embedded cohesive zone response and Γ_p is the extra contribution to the bond toughness arising from plastic dissipation and stored elastic energy within the adhesive layer. The parameters of the model are identified from experiments on two different adhesives exhibiting very different fracture properties. Most of the tests were performed using the wedge-peel test method for a variety of adhesives, adherents and wedge thicknesses. The model captures the constraint effects resulting from the change in Γ_p: (i) the plastic dissipation increases with increasing bond line thickness in the fully plastic regime and then decreases to reach a constant value for very thick adhesive layers; (ii) the plastic dissipation in the fully plastic regime increases drastically as the thickness of the adherent decreases. Finally, this model is used to assess a simpler approach which consists of simulating the full adhesive layer as a single row of cohesive elements.     

Peeling experiments of ductile thin films along ceramic substrates – Critical assessment of analytical models

Two types of peeling experiments are performed in the present research. One is for the Al film/Al₂O₃ substrate system with an adhesive layer between the film and the substrate. The other one is for the Cu film/Al₂O₃ substrate system without adhesive layer between the film and the substrate, and the Cu films are electroplated onto the Al₂O₃ substrates. For the case with adhesive layer, two kinds of adhesives are selected, which are all the mixtures of epoxy and polyimide with mass ratios 1:1.5 and 1:1, respectively. The relationships between energy release rate, the film thickness and the adhesive layer thickness are measured during the steady-state peeling process. The effects of the adhesive layer on the energy release rate are analyzed. Using the experimental results, several analytical criteria for the steady-state peeling based on the bending model and on the two-dimensional finite element analysis model are critically assessed. Through assessment of analytical models, we find that the cohesive zone criterion based on the beam bend model is suitable for a weak interface strength case and it describes a macroscale fracture process zone case, while the two-dimensional finite element model is effective to both the strong interface and weak interface, and it describes a small-scale fracture process zone case.     

Adhesive fracture of a lap shear joint

In many respects, adhesive and cohesive fractures are similar. It has been demonstrated in both cases that a Griffith-type energy balance can often be used to predict failure, e.g., crack growth. The only essential difference involves the interpretation of the energy required to create new (adhesive or cohesive) surface area. In the cohesive case, the specific fracture energy γ _c is that required to create a new surface in the same material, while in the adhesive case, the specific fracture energy γ _a is the energy per unit area required to separate different materials. The mechanical analysis, including a stress analysis to determine the strain energy and energy balance in principle remains unchanged. Generally speaking adhesive-bonded joints involve sharp corners or other “singularities” between adjacent materials which act as stress concentrators, particularly if a crack or other sharp imperfection is present or arises at such a location. The Griffith energy approach circumvents the problem of just how large this mathematically infinite stress must be to initiate failure. Recently, this method had been successfully applied to a number of different adhesive geometries; this paper discusses the case of a single-lap shear joint. This geometry is important because the lap-joint test is a common method for comparing adhesive strengths; in addition, the configuration itself is often used in engineering practice. Adhesive fracture is, therefore, compared on the basis of both energy and maximum stress criteria. Experimental data suggest the former to yield more accurate predictions.     

Pure mode II fracture characterization of composite bonded joints

A new data reduction scheme is proposed for measuring the critical fracture energy of adhesive joints under pure mode II loading using the End Notched Flexure test. The method is based on the crack equivalent concept and does not require crack length monitoring during propagation, which is very difficult to perform accurately in these tests. The proposed methodology also accounts for the energy dissipated at the Fracture Process Zone which is not negligible when ductile adhesives are used. Experimental tests and numerical analyses using a trapezoidal cohesive mixed-mode damage model demonstrated the good performance of the new method, namely when compared to classical data reduction schemes. An inverse method was used to determine the cohesive properties, fitting the numerical and experimental load–displacement curves. Excellent agreement between the numerical and experimental R-curves was achieved demonstrating the effectiveness of the proposed method.     

Mode I Fracture Characterization of Bituminous Paving Mixtures at Intermediate Service Temperatures

This study presents an integrated approach combining experimental tests and numerical modeling to characterize mode I fracture behavior of bituminous paving mixtures subjected to a wide range of loading rates at intermediate temperature conditions. A simple experimental protocol is developed using the semi-circular bending (SCB) test geometry. The local fracture behavior at the initial notch tip of the SCB specimens is monitored using high-speed cameras with a digital image correlation (DIC) system. The DIC results of the SCB fracture tests are then simulated using a finite element method that is incorporated with material viscoelasticity and cohesive zone fracture. Fracture properties are obtained locally at the notch tip by identifying two cohesive zone fracture parameters (cohesive strength and fracture energy) that result in a good agreement between test results and numerical simulations. The results clearly present significant rate-dependent fracture characteristics of bituminous paving mixtures at intermediate service temperatures. This study further demonstrates that fracture properties of viscoelastic materials need to be characterized at the local fracture process zone when they present ductile fracture behavior.     

A microsystem for the fracture characterization of polysilicon at the micro-scale

To characterize the effective fracture energy G_IC of polysilicon wafers at room temperature, an on-chip MEMS test structure has been designed and fabricated. The device can provide fatigue pre-cracking at the notch apex and subsequently impose a monotonical load up to failure. The proposed procedure combines the experimental data with outcomes of numerical simulations. A continuously monitored decrease in stiffness of the system is linked to the crack length and the effective fracture energy for the non-standard geometry of the testing device. An average value of G_IC = 12.0 ± 1.8 N m^?1 is found. These values are then used in numerical micro-scale fracture analyses taking into account the material heterogeneity due to the grain structure and reproducing the crack propagation process with a cohesive approach.     

A refined cohesive zone model that accounts for inertia of cohesive zone of a moving crack

Existing cohesive zone models assume that actual fracture zone of non-zero mass can be modeled by a line segment (cohesive zone) with no mass and inertia. In the present work, a simplified mass-spring model is presented to study inertia effect of cohesive zone on a mode-I steady-state moving crack. It is showed that fracture energy predicted by the present model increases dramatically when a finite limiting crack speed is approached. Reasonable agreement with known experiments indicates that the present model has the potential to catch the inertia effect of cohesive zone which has been ignored in existing cohesive zone models and better simulate dynamic fracture at high crack speed.     

DETERMINATION OF INTERFACIAL MECHANICAL PARAMETERS FOR AN Al/EPOXY/Al2O3 SYSTEM BY USING PEEL TEST SIMULATIONS

Peel test measurements and simulations of the interfacial mechanical parameters for the Al/Epoxy/Al2O3 system are performed in the present investigation. A series of Al film thicknesses between 20 and 250 microns and three peel angles of 90, 135 and 180 degrees are considered. Two types of epoxy adhesives are adopted to obtain both strong and weak interface adhesions. A finite element model with cohesive zone elements is used to identify the interfacial parameters and simulate the peel test process. By simulating and recording normal stress near the crack tip, the separation strength is obtained, Furthermore, the cohesive energy is identified by comparing the simulated steady-state peel force and the experimental result. It is found from the research that both the cohesive energy and the separation strength can be taken as the intrinsic interfacial parameters which are dependent on the thickness of the adhesive layer and independent of the film thickness and peel angle.     

Direct Evaluation of Cohesive Law in Mode I of Pinus pinaster by Digital Image Correlation

The direct identification of the cohesive law in pure mode I of Pinus pinaster is addressed in this work. The approach couples the double cantilever beam (DCB) test with digital image correlation (DIC). Wooden beam specimens loaded in the radial-longitudinal (RL) fracture propagation system are used. The strain energy release rate in mode I (G _I) is uniquely determined from the load–displacement curve by means of the compliance-based beam method (CBBM). This method relies on the concept of equivalent elastic crack length (a _eq) and therefore does not require the monitoring of crack propagation during test. DIC measurements are processed with two different purposes. Firstly, the physical evidence of a _eq is discussed with regard to actual estimation of the crack length based on post-processing full-field displacement measurements. Secondly, the crack tip opening displacement in mode I (w _I) is determined from the displacements near the initial crack tip. The cohesive law in mode I (σ _I???w _I) is then identified by numerical differentiation of the G _I???w _I relationship. The methodology and accuracy on this reconstruction are addressed. Moreover, the proposed procedure is validated by finite element analyses including cohesive zone modelling. It is concluded that the proposed data reduction scheme is adequate for assessing the cohesive law in pure mode I of P. pinaster.     

Cohesive fracture simulation and failure modes of FRP–concrete bonded interfaces

A work-of-fracture method using three-point bend beam (3PBB) specimen, commonly employed to determine the fracture energy of concrete, is adapted to evaluate the mode-I cohesive fracture of fiber reinforced plastic (FRP) composite–concrete adhesively bonded interfaces. In this study, a bilinear damage cohesive zone model (CZM) is used to simulate cohesive fracture of FRP–concrete bonded interfaces. The interface cohesive process damage model is proposed to simulate the adhesive–concrete interface debonding; while a tensile plastic damage model is used to account for the cohesive cracking of concrete near the bond line. The influences of the important interface parameters, such as the interface cohesive strength, concrete tensile strength, critical interface energy, and concrete fracture energy, on the interface failure modes and load-carrying capacity are discussed in detail through a numerical finite element parametric study. The results of numerical simulations indicate that there is a transition of the failure modes controlling the interface fracture process. Three failure modes in the mode-I fracture of FRP–concrete interface bond are identified: (1) complete adhesive–concrete interface debonding (a weak bond), (2) complete concrete cohesive cracking near the bond line (a strong bond), and (3) a combined failure of interface debonding and concrete cohesive cracking. With the change of interface parameters, the transition of failure modes from interface debonding to concrete cohesive cracking is captured, and such a transition cannot be revealed by using a conventional fracture mechanics-based approach, in which only an energy criterion for fracture is employed. The proposed cohesive damage models for the interface and concrete combined with the numerical finite element simulation can be used to analyze the interface fracture process, predict the load-carrying capacity and ductility, and optimize the interface design, and they can further shed new light on the interface failure modes and transition mechanism which emulate the practical application.     

Effects of adhesive thickness on global and local Mode-I interfacial fracture of bonded joints

The interfacial fracture of adhesively bonded structures is a critical issue for the extensive applications to a variety of modern industries. In the recent two decades, cohesive zone models (CZMs) have been receiving intensive attentions for fracture problems of adhesively bonded joints. Numerous global tests have been conducted to measure the interfacial toughness of adhesive joints. Limited local tests have also been conducted to determine the interface traction-separation laws in adhesive joints. However, very few studies focused on the local test of effects of adhesive thickness on the interfacial traction-separation laws. Interfacial toughness and interfacial strength, as two critical parameters in an interfacial traction-separation law, have important effect on the fracture behaviors of bonded joints. In this work, the global and local tests are employed to investigate the effect of adhesive thickness on interfacial energy release rate, interfacial strength, and shapes of the interfacial traction-separation laws. Basically, the measured laws in this work reflect the equivalent and lumped interfacial fracture behaviors which include the cohesive fracture, damage and plasticity. The experimentally determined interfacial traction-separation laws may provide valuable baseline data for the parameter calibrations in numerical models. The current experimental results may also facilitate the understanding of adhesive thickness-dependent interface fracture of bonded joints.     

Analysis of crack growth and crack-tip plasticity in ductile materials using cohesive zone models

Crack initiation and crack growth resistance in elastic plastic materials, dominated by crack-tip plasticity are analyzed with the crack modeled as a cohesive zone. Two different types (exponential and bilinear) of cohesive zone models (CZMs) have been used to represent the mechanical behavior of the cohesive zones. In this work, it is suggested that different forms of CZMs (e.g., exponential, bilinear) are the manifestations of different micromechanisms-based inelastic processes that participate in dissipating energy during the fracture process and each form is specific to each material system. It is postulated that the total energy release rate comprises the plastic dissipation rate in the bounding material and the separation energy rate within the fracture process zone, the latter is determined by CZMs. The total energy release rate then becomes a function of the material properties (e.g., yield strength, strain hardening exponent) and cohesive properties of the fracture process zone (e.g., cohesive strength and cohesive energy), and the form of cohesive zone model (CZM) that determines the rate of energy dissipation in the forward and wake regions of the crack. The effects of material parameters, cohesive zone parameters as well as the form/shape of CZMs in predicting the crack growth resistance and the size of plastic zone (SPZ) surrounding the crack tip are systematically examined. It is found that in addition to the cohesive strength and cohesive energy, the form (shape) of the traction–separation law of CZM plays a very critical role in determining the crack growth resistance (R-curve) of a given material. It is further observed that the shape of the CZM corresponds to inelastic processes active in the forward and wake regions of the crack, and has a profound influence on the R-curve and SPZ.     

Effect of adhesive thickness,adhesive type and scarf angle on the mechanical properties of scarf adhesive joints

The effects of adhesive thickness, adhesive type and scarf angle, which are determined as the main control parameters by the dimensional analysis, on the mechanical properties of a scarf adhesive joint (SJ) subjected to uniaxial tensile loading are examined using a mixed-mode cohesive zone model (CZM) with a bilinear shape to govern the interface separation. Particularly, the adhesive-dependence of the vital cohesive parameters of CZM, which mainly include initial stiffness, total fracture energy and separation strength, is introduced emphatically. The numerical results demonstrate that the ultimate tensile loading increases as the adhesive thickness decreases. Cross the ultimate tension, the joint loses the load-bearing capacity when adopting the brittle adhesive but sustains partial load-bearing capacity while selecting the ductile adhesive. In addition, for the joint with the ductile adhesive, the maximum applied displacement until the complete failure of it is directly proportional to the adhesive thickness, which is different from the case using the brittle adhesive. Taking the combination of the ultimate loading and applied displacement into account, failure energy is employed to evaluate the joint performances. The results show that the failure energy of the joint with the brittle adhesive increases as the adhesive thickness decreases. Conversely, the situation of the joint using the ductile adhesive is vice versa. Moreover, the effect of the adhesive thickness becomes more noticeable with decreasing the scarf angle owing to the variation of the proportion of each component of the mixed-mode. Furthermore, all the characteristic parameters (the ultimate tensile loading, the maximum applied displacement and the failure energy) that adopted to describe the performances of SJ increase as the scarf angle decreases. Finally, the numerical method employed in this study is validated by comparing with existing experimental results.     

Nonlinear interface shear fracture of end notched flexure specimens

The nonlinear analytical solutions of an end notched flexure adhesive joint or fracture test specimen with identical or dissimilar adherends are investigated. In the current study, a cohesive zone model (with arbitrary nonlinear cohesive laws) based analytical solution is obtained for the interface shear fracture of an end notched flexure (ENF) specimen with sufficiently long bond length. It is found that the scatter and inconsistency in calculating Mode II toughness may be significantly reduced by this model. The present work indicates that the Mode II toughness G_IIc under pure shear cracking condition is indeed very weakly dependent on the initial crack length. And this conclusion is well supported by the experimental results found in the literature. The parametric studies show that the interface shear strength is the most dominant parameter on the critical load. It is also interesting to note that with very short initial crack length and identical interface shear strength, higher Mode II toughness indeed cannot increase the critical load. Unlike the high insensitivity of critical load to the detailed shape of the cohesive law for Mode I peel fracture, the shape of the cohesive law becomes relatively important for the critical load of joints under pure Mode II fracture conditions, especially for joints with short initial crack length. The current study may help researchers deepen the understanding of interface shear fracture and clarify some previous concepts on this fracture mode.     

A Dugdale model based geometrical amplifier enables the measurement of separation-to-failure for a cohesive interface

Regardless of all kinds of different formulae used for the traction-separation relationship in cohesive zone modeling, the peak traction σ_m and the separation-to-failure δ₀ (or equivalently the work-to-separation Γ) are the primary parameters which control the interfacial fracture behaviors. Experimentally, it is hard to determine those quantities, especially for δ₀, which occurs in a very localized region with possibly complicated geometries by material failure. Based on the Dugdale model, we show that the separation-to-failure of an interface could be amplified by a factor of L/r_p in a typical peeling test, where L is the beam length and r_p is the cohesive zone size. Such an amplifier makes δ₀ feasible to be probed quantitatively from a simple peeling test. The method proposed here may be of importance to understanding interfacial fractures of layered structures, or in some nanoscale mechanical phenomena such as delamination of thin films and coatings.     

Strength scaling of adhesive joints in polymer–matrix composites

The fracture of adhesive joints between two glass-fibre laminates was studied by testing double cantilever beam test specimens loaded by uneven bending moments. A large-scale fracture process zone, consisting of a crack tip and a fibre bridging zone, developed. The mixed mode fracture resistance increased with increasing crack length, eventually reaching a steady-state level (R-curve behaviour). The steady-state fracture resistance level increased with increasing amount of tangential crack opening displacement. Cohesive laws, obtained from fracture resistance data, were used for prediction the load carrying capacity of 2-m long “medium size” adhesive joint specimens subjected to four point flexure. Medium size specimens were manufactured and tested. A good agreement was found between the predicted and measured strength values of the medium-size specimens. Thus, the scaling from small specimens to medium-size specimens was successfully achieved.     

Molecular-dynamics simulation-based cohesive zone representation of intergranular fracture processes in aluminum

A traction-displacement relationship that may be embedded into a cohesive zone model for microscale problems of intergranular fracture is extracted from atomistic molecular-dynamics (MD) simulations. An MD model for crack propagation under steady-state conditions is developed to analyze intergranular fracture along a flat Σ99 [1 1 0] symmetric tilt grain boundary in aluminum. Under hydrostatic tensile load, the simulation reveals asymmetric crack propagation in the two opposite directions along the grain boundary. In one direction, the crack propagates in a brittle manner by cleavage with very little or no dislocation emission, and in the other direction, the propagation is ductile through the mechanism of deformation twinning. This behavior is consistent with the Rice criterion for cleavage vs. dislocation blunting transition at the crack tip. The preference for twinning to dislocation slip is in agreement with the predictions of the Tadmor and Hai criterion. A comparison with finite element calculations shows that while the stress field around the brittle crack tip follows the expected elastic solution for the given boundary conditions of the model, the stress field around the twinning crack tip has a strong plastic contribution. Through the definition of a Cohesive-Zone-Volume-Element—an atomistic analog to a continuum cohesive zone model element—the results from the MD simulation are recast to obtain an average continuum traction-displacement relationship to represent cohesive zone interaction along a characteristic length of the grain boundary interface for the cases of ductile and brittle decohesion.     

STOCHASTIC ELASTO-PLASTIC FRACTURE ANALYSIS OF ALUMINUM FOAMS

Model I quasi-static nonlinear fracture of aluminum foams is analyzed by considering the effect of microscopic heterogeneity. Firstly, a continuum constitutive model is adopted to account for the plastic compressibility of the metallic foams. The yield strain modeled by a two- parameter Weibull-type function is adopted in the constitutive model. Then, a modified cohesive zone model is established to characterize the fracture behavior of aluminum foams with a cohesive zone ahead of the initial crack. The tensile traction versus local crack opening displacement relation is employed to describe the softening characteristics of the material. And a Weibull statistical model for peak bridging stress within the fracture process zone is used for considering microscopic heterogeneity of aluminum foams. Lastly, the influence of stochastic parameters on the curve of stress-strain is given. Numerical examples are given to illustrate the numerical model presented in this paper and the effects of Weibull parameters and material properties on J-integral are discussed.     

Theoretical development and experimental validation of a thermally dissipative cohesive zone model for dynamic fracture of amorphous polymers

A thermally dissipative cohesive zone model is developed for predicting the temperature increase at the tip of a crack propagating dynamically in a nominally brittle material exhibiting a cohesive-type failure such as crazing. The model assumes that fracture energy supplied to the crack tip region that is in excess of that needed for the creation of new free surfaces during crack advance is converted to heat within the cohesive zone. Bulk dissipation mechanisms, such as plasticity, are not accounted for. Several cohesive traction laws are examined, and the model is then used to make predictions of crack tip heating at various crack propagation speeds in the nominally brittle amorphous polymer PMMA, observed to fail by a crazing-type mechanism. The heating predictions are compared to experimental data where the temperature field surrounding a high speed crack in PMMA was measured. Measurements are made in real time using a multi-point high speed HgCdTe infrared radiation detector array. At the same time as temperature, simultaneous measurement of fracture energy is made by a strain gauge technique, and crack tip speed is monitored through a resistance ladder method. Material strength can be estimated through uniaxial tension tests, thus minimizing the need for parameter fitting in the stress-opening traction law. Excellent agreement between experiments and theory is found for two of the cohesive traction law temperature predictions, but only for the case where a single craze is active during the dynamic fracture of PMMA, i.e. crack tip speed up to approximately 0.2c_R. For higher speed fracture where subsurface damage becomes prominent, the line dissipation model of a cohesive zone is inadequate, and a distributed damage model is needed.     

Predicting the failure of ultrasonic spot welds by pull-out from sheet metal

A methodology for determining the cohesive fracture parameters associated with pull-out of spot welds is presented. Since failure of a spot weld by pull-out occurs by mixed-mode fracture of the base metal, the cohesive parameters for ductile fracture of an aluminum alloy were determined and then used to predict the failure of two very different spot-welded geometries. The fracture parameters (characteristic strength and toughness) associated with the shear and normal modes of ductile fracture in thin aluminum alloy coupons were determined by comparing experimental observations to numerical simulations in which a cohesive-fracture zone was embedded within a continuum representation of the sheet metal. These parameters were then used to predict the load–displacement curves for ultrasonically spot-welded joints in T-peel and lap-shear configurations. The predictions were in excellent agreement with the experimental data. The results of the present work indicate that cohesive-zone models may be very useful for design purposes, since both the strength and the energy absorbed by plastic deformation during weld pull-out can be predicted quite accurately.