Investigation on the fatigue crack behavior of Zr702/TA2/Q345R composite plate with a crack normal to interface

In this paper, the effects of maximum load, load ratio, and average load on fatigue crack propagation of Zr702/TA2/Q345R composite plate with a crack normal to the interface are studied by experiment and finite element method. When crack propagates to the interface from the compliant material side, the crack growth rate decreases to the minimum at first. After crack penetrates through the interface, the fatigue crack growth rate accelerates continuously. When crack propagates to the interface from the stiff material side, the fatigue crack growth rate generally increases with the crack length. Regardless of the direction of crack growth, the increase of load ratio will weaken the difference of crack growth rate near the interface caused by material property mismatch. Finite element results show that elastic modulus mismatch significantly changes the variation of the stress intensity factor amplitude. All results demonstrate that crack growth rate is dependent on the competition of the stress intensity factor amplitude, the fatigue crack growth rate in the corresponding material, and the interface strength.     

Debonding and crack kinking in foam core sandwich beams—I. Analysis of fracture specimens

Sandwich beam specimens, recently developed for the study of facing/core debond fracture, were analyzed using the finite element method. Peel fracture was approached using a modified double cantilever beam (DCB) sandwich specimen with a precrack between the facing and core, while shear fracture employed a modification of the ASTM block shear test to include a facing/core precrack. Complex and conventional stress intensity factors were calculated for bimaterial cracks located between facing and bondlayer and bondlayer and core over a large range of core moduli. Overall, much larger stress intensity factors were observed for an interfacial crack between the facing and bondlayer than for a crack between the bondlayer and core for both types of specimens. Crack kinking analysis of the DCB specimen revealed that the debond tends to remain interfacial for stiff core materials, but may deflect into the core for compliant core materials. In shear loading of a debonded sandwich beam it was demonstrated that crack kinking is possible for any core material.     

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.     

梯度复合材料裂纹扩展路径和起裂载荷的有限元分析

为了模拟功能梯度材料(FGM)在工程应用中可能会出现的断裂问题并计算相应的开裂载荷,通过编写用户自定义UEL子程序将梯度扩展单元嵌入到ABAQUS软件中模拟功能梯度材料的物理场,并编写交互能量积分后处理子程序计算裂纹尖端的混合模式应力强度因子(SIF),采用最大周向应力准则编写子程序计算裂纹的偏转角,并模拟了裂纹扩展路径,计算了裂纹的起裂载荷。讨论了材料梯度参数对裂纹扩展路径以及起裂载荷的影响规律。通过与均匀材料的对比,验证了功能梯度材料断裂性能的优越性。研究表明:外载平行于梯度方向时,垂直梯度方向的初始裂纹朝着等效弹性模量小的方向扩展,且偏转角在梯度指数线性时出现峰值,并随着组分弹性模量比的增加而变大;当外载和初始裂纹均平行于梯度方向时,材料等效弹性模量和断裂韧性的增加或者梯度指数的减小都导致起裂载荷变大。     

The use of interlayers in modeling interface crack propagation

Delaminations are a common mode of failure at interfaces between two material layers which have dissimilar elastic constants. There is a well-known oscillatory nature to the singularity in the stress fields at the crack tips in these bimaterial delaminations, which creates a lack of convergence in the modewise energy release rates. This makes constructing fracture criteria somewhat difficult. An approach used to overcome this is to artificially insert a thin, homogeneous, isotropic layer (the interlayer) at the interface. The crack is positioned in the middle of this homogeneous interlayer, thus modifying the original ‘bare’ interface crack problem into a companion ‘interlayer’ crack problem. Individual modes I and II energy release rates are convergent and calculable for the companion problem and can be used in the construction of a fracture criterion or locus. However, the choices of interlayer elastic and geometric properties are not obvious. Moreover, a sound, consistent, and comprehensive methodology does not exist for utilizing interlayers in the construction and application of mixed-mode fracture criteria in interface fracture mechanics. These issues are addressed here. The role of interlayer elastic modulus and thickness is examined in the context of a standard interface fracture test specimen. With the help of a previously published analytical relation that relates the bare interface crack stress intensity factor to the corresponding interlayer crack stress intensity factor, a suitable thickness and elastic modulus are identified for the interlayer in a bimaterial four-point bend test specimen geometry. Interlayer properties are chosen to make the interlayer fracture problem equivalent to the bare interface fracture problem. A suitable mixed-mode phase angle and a form for the fracture criterion for interlayer-based interface fracture are defined. A scheme is outlined for the use of interlayers for predicting interface fracture in bimaterial systems such as laminated composites. Finally, a simple procedure is presented for converting existing bare interface crack fracture loci/criteria into corresponding interlayer crack fracture loci.     

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

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

Dynamic fracture of a functionally gradient material having discrete property variation

A functionally gradient material (FGM) with discrete property variation is prepared, and the dynamic fracture in this material is studied using the technique of photoelasticity combined with high-speed photography. Transparent sheets required for the study are made by casting a polyester resin mixed with varying amounts of plasticizer. The mechanical (quasi-static and dynamic) and optical properties of the material are evaluated as a function of the plasticizer content. Results of material characterization show that the fracture toughness increases with increasing plasticizer content, whereas the Young's modulus decreases. The material fringe constant and the dynamic modulus are observed to be relatively insensitive to plasticizer content. The FGM is then prepared by casting together thin strips having different plasticizer content. The dynamic crack propagation phenomenon is studied for four different property variations along the crack propagation direction, and the effects of these property variations on crack speed, crack jump distance and dynamic stress intensity factor are investigated. Results of this investigation show that increasing the toughness in the direction of crack growth reduces the crack jump distance as compared to on increasing-decreasing toughness variation for the same initial energy.     

An experimental investigation of dynamic crack growth past a stiff inclusion

The mechanics of transient crack growth past stiff inclusions embedded in a relatively compliant matrix are studied optically under stress wave dominant loading conditions. An ultra high-speed rotating mirror-type CCD digital camera is used to record gray scales in the crack–inclusion vicinity at rates of up to 300,000 frames per second and 1000 × 1000 pixel resolution in real time. By analyzing the images before and after deformations, crack-tip deformation histories from the time of impact up to complete fracture are mapped and fracture parameters are extracted. The effects of inclusion–matrix adhesion strengths (weak and strong) and eccentricity of the inclusion relative to the crack path in the crack-tip vicinity are examined. A weakly bonded inclusion attracts and traps a dynamically growing mode-I crack momentarily whereas the same is deflected away by the inclusion if it is bonded strongly to the matrix. As a result, significantly higher re-initiation crack velocities are seen in weakly bonded inclusion cases upon re-initiation when compared to the strongly bonded counterparts. The effective stress intensity factor histories extracted from measured full-field displacements show a spike in values corresponding to higher crack velocities. Further, crack-tip mode-mixities correlate well with crack attraction and deflection mechanisms. The measured surface roughness is found to be consistently higher for weakly bonded inclusion specimens compared to the strongly bonded ones.     

Heterogeneity effects on mixed‐mode I/II stress intensity factors and fracture path of laboratory asphalt mixtures in the shape of SCB specimen

Edge cracked semi‐circular shape specimen subjected to three point bend loading is a favourite test specimen for determining fracture toughness of asphalt mixtures. However, in the vast majority of previous experimental works, the homogeneous medium assumption has been considered for determining the stress intensity factor and geometry factors of asphalt mixtures tested with this test configuration. As a more realistic model and in order to consider the effects of heterogeneity on corresponding values of stress intensity factors, the asphalt mixture was modelled as a two‐phase aggregate/mastic heterogeneous mixture and its fracture behaviour was investigated using numerical models of asymmetric semi‐circular bend (ASCB) specimens. The generation and packing algorithm was employed to randomly distribute the aggregates with different shapes and sizes inside the mastic part. The effect of the mechanical properties of asphalt mixture (elastic modulus and the Poisson's ratios of aggregates and mastic), coarse aggregates distribution and crack length were studied on modes I and II geometry factors by means of extensive two‐dimensional finite element analyses. Moreover, the effect of the elastic modulus of asphalt mixture components was evaluated on the fracture path using the maximum tangential stress criterion. It was shown that crack tip location, elastic modulus of aggregates and mastic are the most important affecting parameters on the magnitude of modes I and II geometry factors. It was also shown that the geometry factors are not sensitive to the Poisson's ratios of aggregates and mastic. In addition, fracture cracking path is affected by the elastic modulus of the asphalt mixture components such that, depending on the difference between the stiffness of stiffer coarse aggregates and softer mastic part, the crack may propagate either through the aggregates, mastic or interface of aggregate/mastic.     

On fracture mechanics under complex stress

The majority of linear elastic fracture mechanics investigations since the pioneering work of Irwin and Paris have been carried out under tension-tension loading conditions in sheet metal. However, built up structures have generally been under complex stress conditions and to date very scanty information is available on fracture mechanics parameters under complex stress conditions. The current stale of the art for mixed mode crack tips deformation is reviewed.In order to use linear elastic fracture mechanics methodology to predict crack growth rate in shear webs, an experimental program was initiated. Initial tests on 7075-T6 Aluminum alloy sheet, using a picture frame type specimen, were conducted. The critical stress intensity factors and the rate of crack growth under aforementioned condition are established.     

Inverse problems of material distributions for prescribed apparent fracture toughness in FGM coatings around a circular hole in infinite elastic media

This study is concerned with the inverse problem of calculating material distributions intending to realize prescribed apparent fracture toughness in functionally graded material (FGM) coatings around a circular hole in infinite elastic media. The incompatible eigenstrain induced in the FGM coatings after cooling from the sintering temperature, due to mismatch in the coefficients of thermal expansion, is taken into consideration. An approximation method of determining stress intensity factors is introduced for a crack in the FGM coatings in which the FGM coatings are homogenized simulating the nonhomogeneous material properties by a distribution of equivalent eigenstrain. A radial edge crack emanating from the circular hole in the homogenized coatings is considered for the case of a uniform pressure applied to the surfaces of the hole and the crack. The stress intensity factors determined for the crack in the homogenized coatings represent the approximate values of the stress intensity factors for the same crack in the FGM coatings, and are used in the inverse problem of calculating material distributions in the FGM coatings intending to realize prescribed apparent fracture toughness in the coatings. Numerical results are obtained for a TiC/Al₂O₃ FGM coating, which reveal that the apparent fracture toughness in FGM coatings around a circular hole in infinite elastic media can be controlled within possible limits by choosing an appropriate material distribution profile in the coatings.     

SOME OBSERVATIONS ON SMALL FATIGUE CRACKS IN A SUPERALLOY

Abstract —An investigation into the applicability of linear elastic fracture mechanics to very small fatigue cracks growing in a powder metallurgy nickel base superalloy is described. An unusual specimen was designed to facilitate the study of these small cracks. The stress intensity factor for the specimen was estimated and then calculated from the plastic zone size as determined by interferometry. The crack tip deformation field was also observed in the SEM and by stereoscopic viewing. These observations showed that the macroscopic deformation field was the same for both the long and short cracks, and was controlled by the stress intensity. The fatigue crack tip was found to interact strongly with the material microstructure and the localgrowth rate cannot be correlated with fracture mechanics quantities.     

倾斜应力作用下垂直于功能梯度材料夹层的币型裂纹扩展问题

分析了功能梯度材料中币型裂纹扩展问题。该裂纹体受有与裂纹面成任意角度的张应力或压应力,裂纹垂直于无限域中功能梯度材料夹层。假定非均匀介质的功能梯度材料夹层与两个半无限域完全结合,其弹性模量沿厚度方向变化。利用已发表的裂纹应力强度因子数据和线弹性断裂力学的叠加原理,将应力强度因子耦合于最小应变能密度因子断裂判据,讨论了裂纹扩展的临界荷载;并讨论了荷载方向和材料性质对临界荷载的影响。     

The fracture analysis of a graded coating/substrate system of finite thickness with arbitrary spatial variations of coating properties: Plane deformation

A new multi-layered model for functionally graded materials (FGMs) with continuously varying elastic properties is developed. The model divides the FGM into multiple layers. In each layer the material properties vary linearly and are continuous on the sub-interfaces. With this new multi-layered model, we solve the crack problems of an FGM coated strip under the in-plane deformation. The method employs the Fourier integral transform technique and singular integral equation theory. The stress intensity factors are calculated. Comparisons between the present model and other existing models show some advantages of the new model: (i) it involves no discontinuities of the material properties at the sub-interfaces; and (ii) it can be used to analyze the crack problems of FGMs with properties of arbitrary variations.     

Determination of stress intensity factor solutions for cracks in finite-width functionally graded materials

A generalized method to determine the stress intensity factor equations for cracks in finite-width specimens of functionally graded materials (FGMs), based on force balance in regions ahead of the crack tip is provided. The method uses the Westergaard's stress distribution ahead of the crack in an infinite plate and is based on the requirement of isostrain deformation of layers of varying moduli ahead of the crack tip. It is shown that the modified Westergaard equation describes the normal stress distribution and the singular stress state ahead of the crack tip in a reasonably accurate manner. Based on this, closed-form analytical equations for the stress intensity factors of cracks in finite-width center cracked specimens were derived. Comparisons of the K values from the analytical equations with that obtained from FEM simulations indicate that the derived stress intensity factor equations for FGMs are reasonably accurate. For the finite-width center-cracked-tension (CCT) specimen, the errors are less than 10% for most of the crack lengths for materials with the outer layer modulus ratios varying from 0.2 to 5. The stress intensity factors were found to be sensitive to the absolute values of moduli of the layers, the modulus ratio of the outer layers as well as the nature of gradation including the increasing and the decreasing functional forms. The stress intensity factor equations are convenient for engineering estimates of stress intensity factors as well as in the experimental determinations of fracture toughness of FGMs.     

Dynamic stress intensity factor of a functionally graded material under antiplane shear loading

Summary The dynamic response of a finite crack in an unbounded Functionally Graded Material (FGM) subjected to an antiplane shear loading is studied in this paper. The variation of the shear modulus of the functionally graded material is modeled by a quadratic increase along the direction perpendicular to the crack surface. The dynamic stress intensity factor is extracted from the asymptotic expansion of the stresses around the crack tip in the Laplace transform plane and obtained in the time domain by a numerical Laplace inversion technique. The influence of graded material property on the dynamic intensity factor is investigated. It is observed that the magnitude of dynamic stress intensity factor for a finite crack in such a functionally graded material is less than in the homogeneous material with a property identical to that of the FGM crack plane.     

硫化锌热冲击试验与裂纹间距预报

重点研究了硫化锌热冲击开裂机理和热冲击裂纹间距、深度的预报。10mm厚硫化锌试块的燃气急热试验表明:裂纹间距随热冲击能量的增大而减小,热冲击过程中加热面最先出现非贯穿裂纹,停止加热后,裂纹贯穿试件。结合传热和热强度仿真分析,获得了热冲击过程中试件的瞬态温度场和应力场。基于材料性能的损伤演化理论,以裂纹间距和深度为变量,利用最小能量原理,获得了热冲击裂纹间距的理论预报方法,预测结果与试验吻合较好,进而分析了断裂韧性、热胀系数、材料初始模量对裂纹间距、裂纹深度的影响。该文的研究对深入理解硫化锌的热冲击失效机制,对其改性和研制具有重要意义。     

Investigations into the fracture mechanics of acetylsalicylic acid and lactose monohydrate

The fracture mechanics of acetylsalicylic acid (ASS) and lactose monohydrate (LM) were studied using three-point beam bending experiments and compared with conventional tabletting performance. ASS was found to have an unusual behaviour in terms of its Young's modulus and tensile strength when determined with beams of different porosities. The Young's modulus as a function of beam porosity showed two exponential parts separated by a constant region and the tensile strength as a function of the porosity followed a non-exponential law. Tabletting experiments revealed that ASS undergoes different deformation mechanisms at the different compaction pressures associated with the porosity ranges covering the different regions. The different deformation mechanisms might have caused different crack and flaw patterns or different crack lengths, in particular at the beam surfaces, which are under maximum tensile stress during the tests. The unusual findings were, however, not reflected in experiments to determine the critical stress intensity factor as a function of beam porosity, because here crack propagation is controlled via a notch introduced into the beams. In contrast to ASS, LM behaved like the majority of materials i.e. Young's modulus, tensile strength and critical stress intensity factor were found to relate to the beam porosity exponentially.     

Anti-plane problem of periodic interface cracks in a functionally graded coating-substrate structure

In this paper, the interface cracking between a functionally graded material (FGM) and an elastic substrate is analyzed under antiplane shear loads. Two crack configurations are considered, namely a FGM bonded to an elastic substrate containing a single crack and a periodic array of interface cracks, respectively. Standard integral-transform techniques are employed to reduce the single crack problem to the solution of an integral equation with a Cauchy-type singular kernel. However, for the periodic cracks problem, application of finite Fourier transform techniques reduces the solution of the mixed-boundary value problem for a typical strip to triple series equations, then to a singular integral equation with a Hilbert-type singular kernel. The resulting singular integral equation is solved numerically. The results for the cases of single crack and periodic cracks are presented and compared. Effects of crack spacing, material properties and FGM nonhomogeneity on stress intensity factors are investigated in detail.