On fracture of kinked interface cracks – The role of T-stress

This paper presents a modified maximum tangential stress criterion (MMTS) for prediction of the fracture initiation conditions in kinked bi-material cracks. The criterion takes into account the effect of T-stress as well as the stress intensity factors (K_I and K_II) to predict the mixed mode fracture toughness of interface cracked specimens. First the fracture criterion is developed and the effect of sign and magnitude of T-stress on mixed mode fracture toughness is studied analytically. Then, the suggested criterion is evaluated using the experimental data reported for some epoxy/Aluminum Brazil-nut-sandwich specimens in the literature. The MMTS criterion is also compared with the conventional maximum tangential stress (MTS) criterion and hence, significantly improved estimates were achieved for mixed mode fracture toughness of the tested specimens.     

Crack onset and propagation at fibre–matrix elastic interfaces under biaxial loading using finite fracture mechanics

A new fracture criterion able to predict crack onset and propagation at interfaces between solids is formulated, implemented in a computational code and applied to a particular problem in composites on a microscale. More specifically, this criterion is used to study the debond onset and propagation in mixed mode in the case of a single fibre subjected to a biaxial remote loading. The fracture criterion formulation is based on the Linear Elastic-(Perfectly) Brittle Interface Model (LEBIM) combined with a Finite Fracture Mechanics (FFM) approach, where the stress and energy criteria are suitably coupled. Each of these criteria is a necessary but not sufficient condition for crack onset and propagation. Two empirical mixed-mode fracture criteria are considered and tested: the interface fracture toughness law by Hutchinson and Suo and the quadratic stress criterion. The FFM + LEBIM approach developed offers an adequate characterization of the interface stiffness in contrast to the too restrictive, original LEBIM formulation.     

A criterion for brittle fracture in U-notched components under mixed mode loading

A failure criterion is proposed for brittle fracture in U-notched components under mixed-mode static loading. The criterion, called UMTS, is developed based on the maximum tangential stress criterion and also a criterion proposed in the past for mode I failure of rounded V-shaped notches [Gomez FJ, Elices M. A fracture criterion for blunted V-notched samples. Int J Fracture 2004;127:239-64]. Using the UMTS criterion, a set of fracture curves are derived in terms of the notch stress intensity factors. These curves can be used to predict the mixed mode fracture toughness and the crack initiation angle at the notch tip. An expression is also obtained from this criterion for predicting fracture toughness of U-notched components in pure mode II loading. It is shown that there is a good agreement between the results of UMTS criterion and the experimental data obtained by other authors from three-point bend specimens.     

Verification of a non-local stress criterion for mixed mode fracture in wood

An extension of a non-local stress fracture criterion to orthotropic materials based on the damage model of an elastic solid containing growing microcracks was presented in this paper. By taking this approach, a new fracture condition expressed in terms of the mixed mode stress intensity factors for orthotropic materials was proposed and its applicability to predict of a crack initiation and propagation in wood was validated. Predicted values of the stress intensity factors at failure were compared to experimental observations carried out on wood specimens for cracks arbitrarily oriented with respect to the orthotropy axes. Special considerations were applied to the comparison of the non-local stress fracture criterion with some classical fracture criteria for orthotropic materials.     

Hydrogen effect on fracture toughness of thin film/substrate interfaces

The effect of hydrogen on the interface fracture toughness of two nano-film/substrate structures, Ni/Si and Cu/Si, were evaluated using four-point bend specimens with and without hydrogen charging. Hydrogen typically decreases the fracture toughness of materials. However, we found in this study that the interfacial toughness between the Ni film and the Si substrate increased due to the presence of hydrogen, while that of Cu/Si decreased. Nanoindentation experiments for the Ni and Cu films revealed that local plasticity in the Ni and Cu films is promoted by the charged hydrogen. The critical stress intensity at the Ni/Si interface crack considering the plasticity of Ni, namely the true fracture toughness, is scarcely influenced by the existence of hydrogen. The apparent increase in fracture toughness of the Ni/Si interface is due to the large stress relaxation near the crack tip caused by softening due to the presence of hydrogen. Although the promotion of plastic deformation of Cu relaxes the stress intensity at the Cu/Si interface crack, the apparent interfacial toughness still decreases because of the significant decrease in the true toughness due to the presence of hydrogen.     

混凝土/花岗岩界面Ⅰ-Ⅱ复合型动态断裂试验研究

为研究混凝土/岩石界面在复合型应力条件下的动态断裂性能,考虑四种应变率(10-5~10-2 s-1)及三种模态(21.8°,41.7°和60.3°)工况,对混凝土/花岗岩复合试件进行了四点剪切试验,获得了荷载与裂缝张开位移及裂缝剪切位移的关系曲线;结合界面力学理论和结构动力分析得到了界面Ⅰ型和Ⅱ型动态应力强度因子,据此得到并分析了断裂韧度、应变能释放率的率相关性及模态比相关性。结果表明:在所研究的应变率和模态角范围内,同一时刻的裂缝张开位移均大于裂缝剪切位移;Ⅰ型和Ⅱ型断裂韧度均随应变率的提高而增加,Ⅰ型断裂韧度随模态角的增大而减小,Ⅱ型断裂韧度随模态角的增大而增加;应变能释放率随应变率和模态角的增加均呈现出增长趋势。     

Experimental and numerical investigations on fracture process zone of rock–concrete interface

A crack propagation criterion for a rock–concrete interface is employed to investigate the evolution of the fracture process zone (FPZ) in rock–concrete composite beams under three‐point bending (TPB). According to the criterion, cracking initiates along the interface when the difference between the mode I stress intensity factor at the crack tip caused by external loading and the one caused by the cohesive stress acting on the fictitious crack surfaces reaches the initial fracture toughness of a rock–concrete interface. From the experimental results of the composite beams with various initial crack lengths but equal depths under TPB, the interface fracture parameters are determined. In addition, the FPZ evolution in a TPB specimen is investigated by using a digital image correlation technique. Thus, the fracture processes of the rock–concrete composite beams can be simulated by introducing the initial fracture criterion to determine the crack propagation. By comparing the load versus crack mouth opening displacement curves and FPZ evolution, the numerical and experimental results show a reasonable agreement, which verifies the numerical method developed in this study for analysing the crack propagation along the rock–concrete interface. Finally, based on the numerical results, the effect of ligament length on the FPZ evolution and the variations of the fracture model during crack propagation are discussed for the rock–concrete interface fracture under TPB. The results indicate that ligament length significantly affects the FPZ evolution at the rock–concrete interface under TPB and the stress intensity factor ratio of modes II to I is influenced by the specimen size during the propagation of the interfacial crack.     

T应力对Ⅰ-Ⅱ复合型裂纹扩展的影响

利用最大周向正应力判据MTS重新分析研究了脆性破坏的Ⅰ-Ⅱ复合型裂纹扩展,其中考虑了平行于裂纹方向的非奇异项T应力。以平板中的斜裂纹处于双向受力为研究对象,通过两个方向力的不同组合以及裂纹与受力方向的夹角变换得到包括纯I型和纯II型在内的Ⅰ-Ⅱ复合型裂纹,分析了T应力对裂纹扩展方向以及断裂时的应力强度因子的影响,并将预测结果与现有的实验数据进行了比较。在此基础上,给出了不同T应力条件下通用的Ⅰ-Ⅱ复合型裂纹扩展条件,可用于给定几何试件的脆性断裂判定。分析结果表明:裂纹尖端非奇异项T应力对裂纹扩展的影响是不可忽略的,尤其是对II型断裂的影响更为明显。     

混凝土I型裂缝扩展准则比较研究

针对混凝土I型裂缝扩展问题,分别采用以起裂韧度为参数的裂缝扩展准则、最大拉应力准则以及裂尖处应力强度因子为零的裂缝扩展准则,数值模拟了强度等级C20、C40、C60、C80和C100的混凝土三点弯曲梁裂缝扩展全过程,获取了试件的荷载-裂缝口张开位移(P-CMOD)曲线并与试验结果进行了比较。结果表明,三种准则中以起裂韧度为参数的裂缝扩展准则计算得到的峰值荷载及P-CMOD全曲线与试验结果差别最小。随着混凝土强度等级的提高,最大拉应力准则以及裂尖处应力强度因子为零的裂缝扩展准则计算出的P-CMOD曲线与试验结果相比均有较为明显的偏离,但以起裂韧度为参数的裂缝扩展准则计算结果与试验曲线更为吻合。试验与计算结果表明,以起裂韧度为参数的裂缝扩展准则更适用于不同强度混凝土材料的断裂分析。     

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.     

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.     

Fracture toughness of the + 45° / – 45° interface of a laminate composite

Experiments are carried out to determine the delamination toughness for a crack along the interface between two transversely isotropic materials. The material chosen for study consists of carbon fibers embedded within an epoxy matrix. A crack is introduced between two layers of this material, with fibers in the upper layer along the + 45°-direction and those in the lower layer along the − 45°-direction both with respect to the crack plane. The Brazilian disk specimen is employed in the testing. To calibrate the specimens, stress intensity factors are obtained which result from the applied load, as well as residual curing stresses. It may be noted that all three modes are coupled, leading to a three-dimensional problem. The finite element method and a mechanical M-integral are employed to determine the stress intensity factors arising from the applied load. For the residual stresses, a three-dimensional conservative thermal M-integral is presented for stress intensity factor determination. The stress intensity factors found for the applied load and residual stresses are superposed to obtain a local energy release rate, together with two phase angles. From the load at fracture, the critical interface energy release rate or interface toughness as a function of phase angles ψ and ϕ is determined. Results are compared to a fracture criterion.     

Mechanical and statistical analyses of fracture of whisker-reinforced ceramic-matrix composites

This paper analyzes the fracture toughness of short-fiber reinforced ceramic-matrix composites (CMC). The effects of crack deflection and fiber pullout on matrix cracking are examined using a combination of mechanical and statistical models. First, the stress intensity factors of a deflected crack subjected to closure stress due to fiber pullout are analyzed based upon the mechanical model. Distributed dislocation method is used for the elastic analysis. Since the deflected crack is subjected to biaxial loading, a mixed mode fracture criterion in linear elastic fracture mechanics is applied to calculate the fracture toughness. Secondly, the number of pullout fibers on the fracture surface is treated as a random variable, and the statistical distribution of these fibers has been determined. The pullout force acting on a deflected crack is also obtained as a random variable by assuming a simple mechanism of fiber pullout. The probability of failure of CMC can thus be estimated from the strength characteristics of the fiber and matrix as well as the interface between these two.     

Investigation of mixed mode brittle fracture in rounded-tip V-notched components

A criterion is proposed for brittle fracture analysis in rounded-tip V-notched components. This criterion, called RV-MTS, is developed based on the maximum tangential stress (MTS) criterion proposed earlier for investigating mixed mode brittle fracture in sharp cracks. Using the RV-MTS criterion, a set of fracture curves is presented based on the notch stress intensity factors (NSIFs) for predicting mixed mode and also pure mode II fracture toughness of rounded-tip V-notches. The criterion is also able to predict fracture initiation angles under mixed mode loading. The validity of the criterion is evaluated by several fracture tests performed on the rounded-tip V-notched Brazilian disc (RV-BD) specimens made of PMMA. A good agreement is shown to exist between the theoretical predictions and the experimental results for various notch opening angles and different notch radii.     

Fracture toughness of foams with tetrakaidecahedral unit cells using finite element based micromechanics

Fracture toughness of open-cell foams consisting of tetrakaidecahedral unit cells is predicted by simulating crack propagation using a finite element (FE) based micromechanical model. The inputs to the model are the geometric parameters required to model the repeating unit cell and tensile strength of the foam ligament or strut. Cracks are created by removing certain number of cells pertaining to a crack length. The FE model consists of a local micro-scale region surrounding the crack tip. For an assumed stress intensity factor, the displacements along the boundary of the local model are calculated based on linear elastic fracture mechanics for orthotropic materials. The stresses in the ligaments ahead of the crack tip calculated from this micro-model in conjunction with the tensile strength of the strut material are used to predict fracture toughness. A parametric study with different micro-model sizes and different crack lengths is performed to check for convergence of predicted Mode-I, Mode-II and mixed mode fracture toughness values. The effect of applying rotations as additional boundary conditions along with translational displacement boundary conditions on the predicted fracture toughness values is also studied.     

Fracture toughness of polycrystalline tungsten under mode I and mixed mode I/II loading

The fracture toughness of swaged polycrystalline tungsten was tested parallel and perpendicular to the swaging direction and under mixed mode I/mode II loading. The fracture mode is dominated by the microstructure and changed from all-transgranular cleavage in mode I to almost all-intergranular fracture in mode II. The mixed mode results can be related to two common failure criteria, the maximum tensile stress criterion (Maximum σ) and the maximum energy release rate criterion (Maximum G), but the large scatter in the data prohibits a clear distinction between the two criteria. Tests at 77 K show that the polycrystal is significantly tougher than the single crystal at this temperature. This is a consequence of the deflection of the crack into the grain boundaries and the imperfect texture (as compared to a single crystal) of the polycrystalline material.     

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.     

On the Effect of Hydrogen on the Fracture Toughness of Steel

A model is developed to quantify the effect of hydrogen on the critical stress intensity factor or fracture toughness of steels. The stress-assisted hydrogen diffusion model proposed by Liu (1970) is assumed and combined with the elastic stress field around the crack tip for quantifying the hydrogen concentration at the crack tip. Introducing a fracture criterion as the critical hydrogen concentration at a critical distance ahead of the crack tip, this model is successfully applied to the interpretation of hydrogen embrittlement behavior in a piping material. Experimental data at constant temperature were used to validate the model. With further development, the model has the potential to predict fracture toughness values at temperatures other than the test temperature.     

Significance of K-dominance zone size and nonsingular stress field in brittle fracture

Stress intensity factor has been used to characterize the fracture toughness of a brittle material. This practice is apparently based on the assumption that the singular stress alone at the crack tip is responsible for fracture and that the nonsingular part of the near tip stress has no effect on fracture. In this study, mode I fracture experiments were conducted on a brittle material (PMMA) with four different specimen configurations. The result indicated that fracture toughness cannot be described by stress intensity alone and that a second parameter representing the influence of the nonsingular stress is needed. A two-parameter fracture model was proposed and validated with the experimental result. This two-parameter model was shown to be able to account for various effects created by specimen configurations, crack sizes, and loading conditions, on the fracture behavior of brittle materials.