Fracture parameters for interfacial cracks: an experimental-finite element study of crack tip fields and crack initiation toughness

Crack tip measurements and analysis of interfacial parameters for PMMA-aluminum bimaterial system are presented. A variety of crack tip mode-mixities are obtained by subjecting asymmetric four-point-bend specimens to different boundary loads. The crack tip fields are mapped using the optical method of Coherent Gradient Sensing (CGS). The complex stress intensity factors and the associated crack tip mixities () are measured from CGS fringe patterns. The asymptotic expansion field for interface cracks is used for extracting fracture parameters by accounting for higher order contributions to the experimental data. The measurements are compared with complementary finite element computations. A linear relationship between crack tip mixity and the applied load mixity is experimentally demonstrated in this large elastic mismatch system. The fracture load and hence the energy release rate G _cr () at crack initiation is measured as applied load mixities are varied. Limited discussion on the influence of surface roughness prior to bonding on the fracture toughness is included. Positive and negative shear on the crack plane produce different failure responses in this bimaterial system and the observed asymmetry is akin to the one predicted by the T&H model that includes crack tip nonlinearty.     

Measurement of interfacial fracture parameters using coherent gradient sensing (CGS)

An optical interferometry called coherent gradient sensing (CGS) has been extended for mapping interface crack tip fields and for evaluating fracture parameters. The optical technique is a double grating shearing interferometer with an on line spatial filtering arrangement. The method offers real time full field measurements and can be used both in transmission made and reflection mode. The interferometer measures small angular deflections of light rays which can be further related to in plane gradients of _x + _y in transmission through elasto-optic relations. Direct interfacial crack tip measurements in a high stiffness mismatch PMMA-aluminium bimaterial system are performed. A variety of crack tip mode mixities are studied using asymmetric four point bend specimens subjected to different far field mechanical loads. The. complex stress intensity factors and the associated phase angles are measured from CGS patterns using an asymptotic expansion field. The measurements are compared with finite element results.     

K‐dominance of static crack tip in functionally gradient materials

K‐dominance of static crack tip in functionally gradient materials (FGMs) with a crack oriented along the direction of the elastic gradient is studied through coherent gradient sensing (CGS), digital speckle correlation method (DSCM) and finite element method (FEM). In the direction of crack propagation, the shear modulus has a linear variation with constant mass density and Poisson's ratio. First, the CGS and DSCM governing equations related to the measurements and the elastic solutions at mode I crack in FGMs are obtained in terms of the stress intensity factor, material constants and graded index. Secondly, two kinds of FGMs specimens and one homogenous specimen are prepared to observe the influences of the property variation on the K‐dominance. Then, CGS and DSCM experiments using three‐point‐bending of FGMs and homogenous beams are performed. Thirdly, based on the results of the experiments, the stress intensity factors of three kinds of specimens are calculated by CGS and DSCM. Meanwhile, the stress intensity factors are obtained by FEM. Finally, comparing the results from CGS, DSCM and FEM, the K‐dominance of mode‐I static crack tip in FGMs is discussed in detail.     

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.     

On the fatigue and fracture behavior of necked double shear lugs for aircraft applications

The fatigue and fracture behavior of double shear lugs subjected to axial loading is investigated. The focus is on specific shapes, so-called waisted or necked lugs. These structural components used in aircraft interior are prone to fatigue loads. Three different sizes of necked double shear lugs made of high strength aluminum 2024-T351 and steel 17–4 PH are tested using constant amplitude cyclic loadings with a load ratio R = 0.01. Measurement data is used to identify the number of cycles to crack initiation and final fracture. Fatigue tests show that cracks initiate either at the inside or outside surface of necked lugs. However, no clear dependency on the load amplitude, lug size and material could be found. Numerical simulations using both conventional finite element method (FEM) and extended finite element method (XFEM) are performed to calculate the stress intensity factors (SIFs) for multiple crack lengths of straight and necked double shear lugs. Calculated stress intensity factors for straight lugs fit well to stress intensity factors reported in literature. Stress intensity factor curves of inside and outside cracks of necked lugs plotted with respect to crack length, cross each other, which could have an influence on the fracture behavior observed in fatigue tests.     

Quasi-static and dynamic fracture of graphite/epoxy composites: An optical study of loading-rate effects

Strain-rate effects on fracture behavior of unidirectional composite materials are studied. Single-edge notched multi-layered unidirectional graphite composites (T800/3900-2) are investigated to examine fracture responses under static and dynamic loading conditions using a digital speckle correlation method. The fracture parameters for growing cracks are extracted as a function of fiber orientation. A 2D digital image correlation (DIC) method is used to obtain time-resolved full-field in-plane surface displacements when specimens are subjected to quasi-static and impact loading. Stress intensity factor and crack extension histories for pure mode-I and mixed mode cases are extracted from the full-field displacements. When compared to the dynamic stress intensity factors at crack initiation, the static values are found to be consistently lower. The stress intensity factor histories exhibit a monotonic reduction under dynamic loading conditions whereas an increasing trend is seen after crack initiation under quasi-static loading cases. This is potentially due to dominant crack face fiber bridging effects in the latter cases.     

Dynamic fracture of graphite/epoxy composites stiffened by buffer strips: An experimental study

Fracture responses of unidirectional graphite/epoxy composite coupons enhanced by buffer strips are investigated under impact loading conditions using digital image correlation technique and high-speed photography. Composite coupons made of phenylethynyl terminated imide oligomer (PETI-5) as matrix and IM7 graphite fiber as reinforcement are studied. Buffer strips are made of the same material but with a different stacking sequence to attain quasi-isotropy. Edge-notched coupons are subjected to impact loading along the axis of symmetry. The effectiveness of methods used for attaching the buffer strip, namely, co-curing at elevated temperatures and adhesive bonding at room temperature, are also examined. The optically measured stress intensity factor histories reveal that both methods provide nearly identical fracture responses. However, the crack initiates much later in coupons stiffened using adhesive bonding method than its co-cured counterpart and thus shows higher stress intensity factor at initiation. The residual stresses are shown to be responsible for the difference in the fracture responses.     

Interface fracture properties of a bimaterial ceramic composite

In this investigation, the interface fracture toughness is measured for a pair of ceramic clays which are joined together. The Brazilian disk specimen, which provides a wide range of mode mixity, is employed to measure these properties. Calibration equations relating the stress intensity factors to the applied load and geometry are determined by means of the finite element method and the M-integral. The effect of residual stresses is accounted for by employing a weight function to obtain the contribution to the stress intensity factors. Total stress intensity factors are obtained by superposition. These are employed to determine the critical interface energy release rate as a function of mode mixity from critical data obtained from tests carried out on the Brazilian disk specimens. An energy release rate fracture criterion is compared to the experimental results for .     

An analytical and experimental study of the plate tearing mode of fracture

Certain analytical and experimental aspects of the fracture of cracked thin plates subjected to pure twisting moments are examined. A simplified analytical and finite element approach to evaluate plate tearing mode stress intensity factors is proposed. A photoelastic study was also performed to observe the crack-tip fringe patterns and evaluate the plate tearing mode stress intensity factors. Although the observed fringe patterns differed considerably from the predictions obtained using Williams' analysis, they were much closer to the predictions obtained using Reissner's bending theory and the approach proposed in this paper. The finite-element study using the proposed method as well as the Kirchoff bending theory showed that the stress intensity factors obtained using the proposed method agree more closely with the photoelastic results.     

Antiplane crack analysis of a functionally graded material by a BIEM

Elastostatic analysis of an antiplane crack in a functionally graded material (FGM) is performed by using a hypersingular boundary integral equation method (BIEM). An exponential law is applied to describe the spatial variation of the shear modulus of the FGM. A Galerkin method is applied for the numerical solution of the hypersingular traction BIE. Both unidirectional and bidirectional material gradations are investigated. Stress intensity factors for an infinite and linear elastic FGM containing a finite crack subjected to an antiplane crack-face loading are presented and discussed. The influences of the material gradients and the crack orientation on the stress intensity factors are analyzed.     

Numerical analysis of fracture in ceramic coatings subjected to thermal loading

In this paper the general purpose finite element code ANSYS has been employed to analyse fracture in ceramic coatings subjected to thermal loading. An approach is developed in which hypothetical material properties have been considered as material data for coupled (thermal and structure) finite element analysis. These properties were chosen by assumed changes in some functional properties of ZrO₂-G.G. coatings. The aim was to evaluate the stress intensity factors in different coatings. Furthermore, to demonstrate the influence of crack length and coating geometry on the stress intensity in coatings, finite element analyses were carried out for various cases. The normalized stress intensity factors were obtained. The results showed that the shorter the crack length and the thinner the coating, the sounder the coatings. Furthermore, coatings representing a wide range of thermal and mechanical properties have a close normalized stress intensity factor values. It is also concluded that the finite element technique can be used to optimize the design and the processing of ceramic coatings.     

Specimen size effects on the determination of KIc-values in the range of elastic-plastic material behavior

A new fracture mechanics evaluation method, (method of specific potential energy) is introduced, which enables one to predict the fracture load of large specimens in the range of elastic-plastic material behavior. This method is discussed using test results obtained from CT-specimens of the steels 22 Ni Mo Cr 37 and A 533 BI. Also, fracture mechanics data published in the literature were evaluated using the above method. These measurements had been performed on several titanium and aluminum alloys using CT-specimens, SENB-specimens, and CCT-specimens. In all cases a relation between the potential energy at the point of fracture and the net cross sectional area is found. The analytical form of this relation permits the derivation of relationships for evaluating maximum stress intensity factors or fracture loads for arbitrary specimen sizes. The results show that a maximum stress intensity factor can be derived which is dependent on the specimen dimensions. This method is recommended in the case of elastic-plastic material behavior for the evaluation of critical stress intensity factors K_Ic, which fulfils the requirements of ASTM E 399-74; moreover, the method seems to be useful for the evaluation of fracture loads of thin-walled sheets containing cracks.     

Effect of compressive transverse normal stress on mode II fracture toughness in polymeric composites

Effect of transverse normal stress on mode II fracture toughness of unidirectional fiber reinforced composites was studied experimentally in conjunction with finite element analyses. Mode II fracture tests were conducted on the S2/8552 glass/epoxy composite using off-axis specimens with a through thickness crack. The finite element method was employed to perform stress analyses from which mode II fracture toughness was extracted. In the analysis, crack surface contact friction effect was considered. It was found that the transverse normal compressive stress has significant effect on mode II fracture toughness of the composite. Moreover, the fracture toughness measured using the off-axis specimen was found to be quite different from that evaluated using the conventional end notched flexural (ENF) specimen in three-point bending. It was found that mode II fracture toughness cannot be characterized by the crack tip singular shear stress alone; nonsingular stresses ahead of the crack tip appear to have substantial influence on the apparent mode II fracture toughness of the composite.     

An insight into mode II fracture toughness testing using SCB specimen

The effect of friction forces between the test specimen and its bottom supports on the mode II fracture toughness values obtained using the semicircular bend (SCB) specimen is investigated. First, a number of experiments were conducted on SCB specimen in order to determine the mode II fracture toughness of polymethyl methacrylate (PMMA) according to the conventional approaches available in the literature. Three different types of supports that have been frequently employed by researchers in recent years were used to evaluate the effect of support type on the fracture loads. It was found that the friction forces between the supports and the SCB specimen have a significant effect on the value of mode II fracture toughness measured using the SCB samples. Then, the specimen was simulated using finite element method for more detailed investigation on the near crack tip stress field evolution when friction forces increase between the supports and the SCB specimen. The finite element results confirmed that the type of support affects not only the stress intensity factors K_I and K_II but also the T‐stress. The experimental and numerical results showed that the use of the crack tip parameters available in literature for frictionless contact between the supports and the SCB specimen can result in significant errors when the mode II experiments are performed by using the fixed or roller‐in‐grove types of supports.     

Fracture of anodic-bonded silicon-thin film glass-silicon triple stacks

In this study we focus on the fracture behavior of two types silicon-thin film glass-silicon (Si-Glass-Si) triple stacks specimens with a sharp corner. We determine the notch stress intensity factor Kⁿ for both specimens using a combination of the Williams eigenfunction expansion method, Stroh’s sextic formalism, finite element analysis, and the path-independent H-integral. Empirical solutions of dimensionless stress intensity factors are proposed for two typical specimens, and the dependence of geometry is analyzed. Furthermore, the effect of glass thickness on stress intensity is explored for anodic-bonded Si-Glass-Si triple stacks. We discuss the feasibility of using a critical value of Kⁿ to correlate the failure results for both specimens with various bond area and glass thickness.     

An analysis of cracks emanating from a circular hole in unidirectional fiber-reinforced composites

This paper presents an analytical study of cracks emanating from a circular hole in an off-axis unidirectional fiber-reinforced composite. A convenient and accurate method of analysis is formulated on the basis of conservation laws of elasticity and of fundamental relationships in anisotropic fracture mechanics. The problem is eventually reduced to a system of linear algebraic equations in mixedmode stress intensity factors. Superiority of the current analysis to other approaches in investigating the problem with very complicated crack geometry and material anisotropy is demonstrated when used in conjunction with any numerical method such as a finite element analysis. Mixed-mode stress intensity factors and the associated energy release rates in the crack problem are determined for the composites with various fiber orientations. Solutions for both single and double cracks emanating from the edge of a hole in the composites are presented also to illustrate the fundamental nature of the problem.     

Estimation of mixed-mode stress intensity factors using digital image correlation and an interaction integral

This paper presents a technique for the experimental measurement of stress intensity factors in cracked specimens under mixed-mode loading. This technique is based on full-field measurement using digital image correlation and an interaction integral. Such domain-independent integrals are often used in the finite element method to calculate stress intensity factors. The main advantage of this technique is that the errors made in the estimation of the measured displacement field near the cracks tip do not affect the measurement of the stress intensity factors. The capabilities of the method are illustrated through fracture measurements on compact tension specimens made of maraging steel. Another test under mixed-mode loading is presented.     

Analysis of damaged material containing periodically distributed elliptical microcracks by using the homogenization method based on the superposition method

The presence of multiple microcracks in a structural component causes material degradation such as reduction in the stiffness or reduction in the fracture toughness of the component. In this paper, the homogenization method is used to evaluate mechanical properties of the damaged material. The adaptation of the superposition method to the homogenization method is also presented. The proposed method makes use of the finite element solution of uncracked solid and the analytical solution. The effective elastic moduli of damaged materials containing lattice-distribution microcracks are estimated by the proposed method. Furthermore, the stress fields and the stress intensity factors of the elliptical microcracks in the damaged material at a micro-mechanics scale are evaluated to illustrate microscopic behavior such as crack interaction.     

含半椭圆表面裂纹圆柱壳体的三维热弹性动态断裂

研究了含轴向半椭圆表面裂纹的圆柱壳体在热应力与冲击载荷作用下的动态断裂情况,并应用所研制的三维动态断裂有限元程序进行了大规模的数值计算,确定了圆柱壳体的三维温度分布及热-力耦合下的动态应力强度因子,所得结果在一定程度上揭示了热-力作用下圆柱壳体的边界表面、裂纹面、物质惯性和弹性波的相互作用在结构动态断裂中的重要性。