On the analysis of a mixed mode bending sandwich specimen for debond fracture characterization

The mixed mode bending specimen originally developed for mixed mode delamination fracture characterization of unidirectional composites has been extended to the study of debond propagation in foam cored sandwich specimens. The compliance and strain energy release rate expressions for the mixed mode bending sandwich specimen are derived based on a superposition analysis of solutions for the double cantilever beam and cracked sandwich beam specimens by applying a proper kinematic relationship for the specimen deformation combined with the loading provided by the test rig. This analysis provides also expressions for the global mode mixities. An extensive parametric analysis to improve the understanding of the influence of loading conditions, specimen geometry and mechanical properties of the face and core materials has been performed using the derived expressions and finite element analysis. The mixed mode bending compliance and energy release rate predictions were in good agreement with finite element results. Furthermore, the numerical crack surface displacement extrapolation method implemented in finite element analysis was applied to determine the local mode mixity at the tip of the debond.     

Face/core debond fatigue crack growth characterization using the sandwich mixed mode bending specimen

Face/core fatigue crack growth in foam-cored sandwich composites is examined using the mixed mode bending (MMB) test method. The mixed mode loading at the debond crack tip is controlled by changing the load application point in the MMB test fixture. Sandwich specimens were manufactured using H45 and H100 PVC foam cores and E-glass/polyester face sheets. All specimens were pre-cracked in order to define a sharp crack front. The static debond fracture toughness for each material configuration was measured at different mode-mixity phase angles. Fatigue tests were performed at 80% of the static critical load, at load ratios of R = 0.1 and 0.2. The crack length was determined during fatigue testing using the analytical compliance expression and verified by visual measurements. Fatigue crack growth results revealed higher crack growth rates for mode I dominated loading. For specimens with H45 core, the crack grew just below the face/core interface on the core side for all mode-mixities, whereas for specimens with H100 core, the crack propagated in the core or in the face laminate depending on the mode-mixity at the debond crack tip.     

Numerical and experimental investigation of mixed‐mode fracture parameters on silicon nitride using the Brazilian disc test

Engineering applications of ceramics can often involve mixed‐mode conditions involving both tensile and shear loading. Mixed‐mode fracture toughness parameters are evaluated for applicability to ceramics using the Brazilian disc test on silicon nitride. Semi‐elliptical centrally located surface flaws are induced on the disc specimens using Vickers indentation and compression loaded to fracture with varying levels of mode mixity. The disc specimens are modelled via 3D finite element analysis and all three modes of stress intensity factors computed along the crack front, at failure load. We present a numerical and experimental investigation of four widely used mixed‐mode fracture criteria and conclude that the critical strain energy release rate criterion is simple to implement and effective for silicon nitride under mixed‐mode conditions.     

A novel fixture for mixed mode I/II/III fracture testing of brittle materials

A novel test‐loading device was suggested in order to study the fracture behavior of brittle materials under mixed mode I/II/III loading conditions. A version of the compact tension shear specimen was used as the test configuration. Using a three‐dimensional finite element analysis, the influence of mode mixity on the stress intensity factors, the T‐stress, and 3‐D plastic zone around the crack tip was investigated. In addition, an experimental study was performed on an epoxy polymer using the proposed setup. Finally, the fracture toughness of pure epoxy was measured under several loading conditions. The numerical and experimental results manifested that the proposed setup is able to determine a full range of mixed mode I/II/III fracture properties. At the end, the fracture envelope obtained using the practical study was compared with various three‐dimensional fracture criteria. A negligible discrepancy was concluded between the practical data and the theoretical data estimated by the maximum mean principle stress criterion.     

泡沫夹芯复合材料梁界面裂纹曲折扩展实验与数值模拟

采用双悬臂梁(DCB)试验研究了具有不同密度的PMI泡沫芯体的玻璃纤维增强复合材料夹芯梁界面裂纹曲折破坏路径。基于包含裂纹的物质点算法(MPM), 建立了与试验研究相适应的MPM模型, 在不同的面板/芯体模量比下计算了界面裂纹裂尖模态比和曲折破坏角, 并结合曲折破坏准则模拟了界面裂纹曲折破坏路径。数值模拟结果和试验现象吻合良好, 说明了本文中数值分析模型和方法的有效性。研究结果表明, 面板材料和芯体材料模量失配越严重, 界面裂纹发生曲折破坏时的破坏角越大; 裂纹折入芯体后, 在 Ⅰ 型为主的加载模式的支配下以基本平行于界面的方向扩展。      

Face sheet debonding in CFRP/PMI sandwich structures under quasi-static and fatigue loading considering residual thermal stress

The face sheet debonding behaviour under quasi-static and fatigue loading in sandwich structures consisting of Carbon Fibre Reinforced Polymer face sheets and a Polymethacrylimid foam core is investigated. The sandwich structure is tested under global mode I and global mode II loading using the Single Cantilever Beam test and the Cracked Sandwich Beam test. Because of the different thermal expansion behaviour of the face sheets and the foam core thermal stresses occur already after the manufacturing process. The impact of these temperature loads on the crack propagation behaviour is investigated via evaluating the experiments numerically with Finite Element Analysis and Virtual Crack Closure Technique.     

On the failure of cracks under mixed-mode loads

Fracture of plates containing a crack under mixed-mode, I and II, loading conditions is investigated. Fracture mechanisms are first examined from fracture surface morphology to correlate with the macroscopic fracture behavior. Two distinct features are observed and they are typical of shear and tensile types of failure. From this correlation, a fracture criterion based on the competition of the attainment of a tensile fracturing stress σ_{_C} and a shear fracturing stress τ_{_C} at a fixed distance around the crack tip is proposed. Material ductility is incorporated using τ_{_C}/σ_{_C} determined from classical material failure theories. The type of fracture is predicted by comparing τ_{_max}/σ_{_max} at r=r_{_C} for a given mixed mode loading to the material ductility_{τ_C/σ_C} , i.e. τ_{_max}/σ_{_max})<(τ_{_C} /σ_{_C}) for tensile type of fracture and (τ_{_max}/σ_{_max}) r (τ_{_C}/ σ_{_C}) for shear type of fracture. It is found that, for typical engineering structural metals with certain ductility, (1) crack propagation initiates according to the maximum hoop stress criterion when the the mode mixity is near mode I and according to the maximum shear stress criterion when the mode mixity is near mode II, and (2) the transition of the failure from tensile to shear type can be predicted by the proposed criterion. For brittle materials the maximum hoop (opening) stress always reaches the tensile fracturing stress before the maximum shear stress reaches the shear fracturing stress of the material at a crack tip. Therefore, specimens made of brittle materials tend to fail under the maximum hoop stress criterion, as demonstrated by Erdogan and Sih (1963) and others. This revised version was published online in August 2006 with corrections to the Cover Date.     

Interface crack in sandwich specimen

Fracture of a sandwich specimen loaded with axial forces and bending moments is analyzed in the context of linear elastic fracture mechanics. A closed form expression for the energy release rate for interface cracking of a sandwich specimen with isotropic face sheets is found from analytical evaluation of the J-integral. An approach is applied, whereby the mode mixity for any combination of the loads can be calculated analytically when a load-independent phase angle has been determined. This load-independent phase angle is determined for a broad range of sandwich configurations of practical interest. The load-independent phase angle is determined using a novel finite element based method called the crack surface displacement extrapolation method. The expression for the energy release rate is based on the J-integral and certain stress distributions along the ends of the sandwich specimen. When the stresses from the crack tip interacts with the stresses at the ends, the present analytical calculation of the J-integral becomes inaccurate. The results show that for the analytically J-integral to be accurate the crack tip must be a certain distance away from the uncracked end of the specimen. For a sandwich specimen with face sheet/core stiffness ratio of 100, this distance is in the order 10 times the face sheet thickness. For sandwich structures with face sheet/core stiffness ratio of 1,000, the distance is 30 times the face sheet thickness.     

J-Dominance in Mixed Mode Ductile Fracture Specimens

The asymptotic mixed mode crack tip fields in elastic-plastic solids are scaled by the J-integral and parameterized by a near-tip mixity parameter, M _{_p} . In this paper, the validity and range of dominance of these fields are investigated. To this end, small strain elastic-plastic finite element analyses of mixed mode fracture are first performed using a modified boundary layer formulation. Here, a two term expansion of the elastic crack tip field involving the stress intensity factor |K| the elastic mixity parameter M _{_e} as well as the T-stress is prescribed as remote boundary conditions. The analyses are conducted for different values of M _{_e} and the T-stress. Next, several commonly used mixed mode fracture specimens such as Compact Tension Shear (CTS), Four Point Bend (4PB), and modified Compact Tension specimen are considered. Here, the complete range of loading from contained yielding to large scale yielding is analyzed. Further, different crack to width ratios and strain hardening exponents are considered. The results obtained establish that the mixed mode asymptotic fields dominate over physically relevant length scales in the above geometries, except for predominantly mode I loading and under large scale yielding conditions. This revised version was published online in August 2006 with corrections to the Cover Date.     

Experimental investigation of compression failure of sandwich specimens with face/core debond

An experimental study of the in-plane compressive failure mechanism of foam cored sandwich specimens with an implanted through-width face/core debond is presented. Tests were conducted on sandwich specimens with glass/vinylester and carbon/epoxy face sheets over various PVC foam cores. Observation of the response of the specimens during testing showed that failure occurred by buckling of the debonded face sheet, followed by rapid debond growth towards the ends of the specimen. The compression strength of the sandwich specimens containing a debond decreased quite substantially with increasing debond size. A high-density core resulted in less strength decrease at any given debond size. Examination of the failure surfaces after separation of the face sheet and core revealed traces of core material deposited on the face sheet evidencing cohesive core failure. The amount of core material adhered to the face sheet decreased with increasing foam density indicating increasing tendency for core/resin interfacial failure.     

Fracture mechanics‐based progressive damage modelling of adhesively bonded fibre‐reinforced polymer joints

A quasi‐static progressive damage model for prediction of the fracture behaviour and strength of adhesively bonded fibre‐reinforced polymer joints is introduced in this paper. The model is based on the development of a mixed‐mode failure criterion as a function of a master R‐curve derived from the experimental results obtained from standard fracture mechanics joints. Consequently, the developed failure criterion is crack‐length and mode‐mixity dependent, and it takes into account the contribution of the fibre‐bridging effect. Energy release rate values for adhesively bonded double‐lap joints are obtained by using the virtual crack closure technique method in a finite element model, and the numerically obtained strain energy release rate is compared to the critical strain energy release rate given by the mixed‐mode failure criterion. The entire procedure is implemented in a numerical algorithm, which was successfully used for predicting the strength and R‐curve response of adhesively bonded double‐lap structural joints made of pultruded glass fibre‐reinforced polymers and epoxy adhesives.     

Analysis of beam-type fracture specimens with crack-tip deformation

A novel bi-layer beam model is developed to account for local effects at the crack tip of a bimaterial interface by modeling a bi-layer composite beam as two separate shear deformable beams. The effect of interface stresses on the deformations of sub-layers, which is referred to as the elastic foundation effect in the literature, is considered in this model by introducing two interface compliance coefficients; thus a flexible joint condition at the crack tip is considered in contrast to the rigid joint condition used in the conventional bi-layer model. An elastic crack tip deformable model is presented, and the closed-form solutions of local deformation at the crack tip are then obtained. By applying this novel crack tip deformation model, the new terms due to the local deformations at the crack tip, which are missing in the conventional composite beam solutions of compliance and energy release rate (ERR) of beam-type fracture specimens, are recovered. Several commonly used beam-type fracture specimens are examined under the new light of the present model, and the improved solutions for ERR and mode mixity are thus obtained. A remarkable agreement achieved between the present and available solutions illustrates the validity of the present study. The significance of local deformation at the crack tip is demonstrated, and the improved solutions developed in this study provide highly accurate predictions of fracture properties which can actually substitute the full continuum elasticity analysis such as the finite element analysis. The new and improved formulas derived for several specimens provide better prediction of ERR and mode mixity of beam-type fracture experiments.*Author for correspondence (E-mail address: qiao@uakron.edu)     

Study of Fatigue Behavior of Epoxy‐Carbon Composites under Mixed Mode I/II Loading

This paper presents an experimental assessment of the initiation and propagation of interlaminar cracks under mixed mode I/II dynamic fracture loading of a composite material with an MTM45‐1 epoxy matrix and unidirectional IM7 carbon‐fiber reinforcement. The aims of the experimental program developed for this purpose are to determine, on the one hand, the initiation curves of the fatigue delamination process, understood as the number of load cycles needed to generate a fatigue crack, and on the other, the crack growth rate (delamination rate) for different percentages of static Gc, in both cases for two mode mixities (0.2 and 0.4) and for a tensile ratio R = 0.1. All this with the goal of quantifying the influence of the degree of mode mixity on the overall behavior of the laminate under fatigue loading. The results show that the energy release rate increases with increasing loading levels for both degrees of mode mixity and that the fatigue limit is located around the same percentages. However, crack growth rate behavior differs from one degree of mode mixity to the other. This difference in the behavior of the material may be due to the varying influence of mode I loading on the delamination process.

     

Mechanical degradation of foam-cored sandwich materials exposed to high moisture

Sandwich specimens composed of E-glass/polyester face sheets bonded to a PVC foam core were exposed to high moisture (95% RH) and immersed in sea-water for extended periods of time. Degradation of mechanical properties of the face sheets, foam core and face/core interface were progressively evaluated using flexural testing of the laminates, through-thickness tension of the foam core and interfacial sandwich DCB fracture testing. Testing reveals substantial flexural stiffness and strength reductions for the laminated composites, and only minor reduction in the tensile stiffness and strength of the foam. Degradation of the interfacial face/core fracture toughness is weak for specimens subjected to elevated moisture and more pronounced for sandwich specimens immersed in sea-water. After 30 days of exposure to high moisture, foam damage is visible in the form of cracks and pits on the cell walls. Optical examinations of expansional strains show that moisture absorbed by the foam penetrates only about to 2–3 mm from the core free surface for the 95% RH condition, while penetrates deeply for the immersed condition.     

Connecting the essential work of fracture, stress intensity factor, Hill’s criterion in mixed mode I/II loading

Ductile sheet structures are frequently subjected to mixed mode loading, resulting that the structure is under the influence of a mixed mode stress field. Instances of interest are when stable crack growth occurs and when the crack-tip is propagating in this complex mixed-mode condition, prior to final fracture. Purposely designed apparatus was built to test thin-sheets of steel (Grade: DX51D) under mixed-mode I/II. These tests, under plane stress conditions, also investigated the effect of thickness on the specific essential work of fracture or the fracture toughness of the material under quasi-static cracking conditions. The fracture toughness is evaluated under incremental mixed-mode loading conditions. The direction of the propagating crack path and fracture type were observed and discussed as the loading mixity was varied. Whilst the specific essential work of fracture or fracture toughness was obtained using the energy approach, the theoretical analysis of the fracture type and direction of crack path were based on the crack tip stresses and fracture criterions of maximum hoop stress and maximum shear stress along with the utilisation of Hill’s theory. For mixed-mode I/II loading, the variation in the fracture toughness contributions ratios are evaluated and used predicatively using the established energy criterion approach to the crack tip stress intensity approach. The comparison between the theoretical directions of the crack path, failure mode propagation are in good agreement with those obtained from experimental testing indicating the definite link between both approaches.     

Crack path selection in adhesively bonded joints: the roles of external loads and speciment geometry

This paper investigates the roles of external loads and specimen geometry on crack path selection in adhesively bonded joints. First, the effect of mixed mode fracture on crack path selection is studied. Using epoxy as an adhesive and aluminum as the adherends, double cantilever beam (DCB) specimens with various T-stress levels are prepared and tested under mixed mode fracture loading. Post-failure analyses on the failure surfaces using X-ray photoelectron spectroscopy (XPS) suggest that the failure tends to be more interfacial as the mode II fracture component in the loading increases. This fracture mode dependence of the locus of failure demonstrates that the locus of failure is closely related to the direction of crack propagation in adhesive bonds. Through analyzing the crack trajectories in failed specimens, the effect of mixed mode fracture on the directional stability of cracks is also investigated. The results indicate that the direction of the crack propagation is mostly stabilized when more than 3% of mode II fracture component is present at the crack tip regardless of the T-stress levels in the specimens for the material system studied. Second, using a high-speed camera to monitor the fracture sequence in both quasi-static and low-speed impact tests, the effect of debond rate on the locus of failure and directional stability of cracks is investigated. Post-failure analyses including XPS, Auger electron spectroscopic depth profile, and scanning electron microscopy indicate that as the crack propagation rate increases, the failure tends to be more cohesive and the cracks tend to be directionally unstable. Last, as indicated by the finite element analyses results, the T-stresses, and therefore the directional stability of cracks in adhesive bonds, are closely related to the thickness of the adhesive layer and also the thickness of adherend. This specimen geometry dependence of crack path selection is studied analytically and is verified experimentally.     

Failure mode of laser welds in lap‐shear specimens of high strength low alloy (HSLA) steel sheets

In this paper, the failure mode of laser welds in lap‐shear specimens of non‐galvanized SAE J2340 300Y high strength low alloy steel sheets under quasi‐static loading conditions is examined based on experimental observations and finite element analyses. Laser welded lap‐shear specimens with reduced cross sections were made. Optical micrographs of the cross sections of the welds in the specimens before and after tests are examined to understand the microstructure and failure mode of the welds. Micro‐hardness tests were also conducted to provide an assessment of the mechanical properties in the base metal, heat‐affected and fusion zones. The micrographs indicate that the weld failure appears to be initiated from the base metal near the boundary of the base metal and the heat‐affected zone at a distance away from the pre‐existing crack tip, and the specimens fail due to the necking/shear of the lower left load carrying sheets. Finite element analyses based on non‐homogenous multi‐zone material models were conducted to model the ductile necking/shear failure and to obtain the J integral solutions for the pre‐existing cracks. The results of the finite element analyses are used to explain the ductile failure initiation sites and the necking/shear of the lower left load carrying sheets. The J integral solutions obtained from the finite element analyses based on the 3‐zone finite element model indicate that the J integral for the pre‐existing cracks at the failure loads are low compared to the fracture toughness and the specimens should fail in a plastic collapse or necking/shear mode. The effects of the sheet thickness on the failure mode were then investigated for laser welds with a fixed ratio of the weld width to the thickness. For the given non‐homogenous material model, the J integral solutions appear to be scaled by the sheet thickness. With consideration of the plastic collapse failure mode and fracture initiation failure mode, a critical thickness can be obtained for the transition of the plastic collapse or necking/shear failure mode to the fracture initiation failure mode. Finally, the failure load is expressed as a function of the sheet thickness according to the governing equations based on the two failure modes. The results demonstrate that the failure mode of welds of thin sheets depends on the sheet thickness, ductility of the base metal and fracture toughness of the heat‐affected zone. Therefore, failure criteria based on either the plastic collapse failure mode or the fracture initiation failure mode should be used cautiously for welds of thin sheets.     

Debonding and crack kinking in foam core sandwich beams—II. Experimental investigation

Debonding and crack kinking in sandwich beams was experimentally examined, and also analyzed using the finite element method. Double cantilever beam (DCB) and shear fracture specimens employing aluminum facings bonded to a wide range of PVC and PMI foam cores using two types of adhesives were considered. It was found that the Young modulus of the core has a profound effect on the tendency of the facing/core interfacial crack to deflect (kink) into the core in DCB testing. In shear testing, crack kinking occurred for all core materials considered. The type of adhesive strongly influences the debond fracture resistance, but not the kink resistance and kink angle. The critical load for onset of kinking increased with increased core density. Finite element analysis of the fracture specimens enabled determination of mixed mode interfacial fracture toughness for the specimens that failed by debonding. For specimens that failed by kinking, interfacial stress intensity factors at the onset of kinking were determined. Measured kink angles compared favorably with kink angles calculated based on the interfacial stress intensity factors prior to kinking.     

Experimental study on fatigue failure and damage of sandwich structure with PMI foam core

Sandwich structures consisting of aluminium skin sheets and polymethacrylimide foam core have been gradually used in the high‐speed trains. The static mechanical properties and fatigue damage of the sandwich structures with polymethacrylimide foam core were experimented in three‐point bending and were discussed. The failure mode is identified as local indentation. The static strength was obtained, and it showed good consistency with the forecasting formula. The fatigue property and damage evolution were also researched under cyclic loading. The fatigue life curve and the fitting formula were submitted. The fatigue damage evolution started from the skin sheet fracture and then the foam core indentation. The displacement at the midpoint as the damage parameter was discussed, and the evolution prediction formula was submitted, which showed great agreement with the experimental results.     

Specimen proposals for mixed mode testing of adhesive layer

The experimental methods to determine the fracture properties for adhesives under mixed mode loading is not as well established as compared to such methods for adhesives under pure mode loading. Some controversies exist regarding the decomposition of the mode mixity. For a flexible linear elastic adhesive, the mode mixity of a single-layer adhesive joint is directly related to the deformation of the adhesive layer at the crack tip. The governing equations for linear elastic single-layer adhesive joints show that the mode mixity depends on the external loads, the properties of the adherends and often on the flexibility of the adhesive layer. This implies some fundamental problems that have to be addressed before an experimental method can be established. The purpose of this paper is to investigate different specimen configurations for mixed mode loading. Requirements for the design of a specimen configuration are given. A new specimen configuration is proposed based on the geometry of a semi-infinite symmetric DCB-specimen. According to this study, the proposed test specimen offers exceptional flexibility, variety and stability.