Criteria for brittle fracture in biaxial tension

The criteria of maximum tangential stress, maximum tangential principal stress, maximum tangential strain and strain energy density are applied to the problems of slit and elliptical cracks under remote uniform biaxial tension. The predicted direction of crack extension and the critical load are compared with experimental results reported by other investigators. The unstable crack paths are determined. The four criteria differ in the case of unequal tension; the strain energy density criterion is the least satisfactory. The criteria of maximum tangential strain and strain energy density can be modified to give a good prediction of critical load.     

Comparison of the criteria for mixed mode brittle fracture based on the preinstability stress-strain field

Prediction of the angle of initial crack extension, critical load and unstable crack paths based on the criteria of maximum tangential stress (MTS), maximum tangential principal stress (MTPS), maximum tangential strain (MTSN), and strain energy density (SED) are compared for slit and elliptical cracks under pure shear loading and elliptical cracks under uniaxial compressive loading. Results presented here complement those in Part I of this investigation. Some of the theoretical predictions have been compared with data available in the literature.All the four criteria are found to be more or less equally applicable in the cases studied for the prediction of direction of initial crack extension and critical load. The unstable crack paths based on the four criteria differ, the difference being greatest for the SED criterion. Some difficulties are found on applying this criterion to some situations.

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Résumé On considère des fissures en entaille et elliptiques soumises à des charges de cisaillement pur et des fissures elliptiques soumises à des charges de compression uniaxiale. On établit une comparaison des prédictions de l'angle d'extension initiale de la fissure, de la charge critique et des chemins de fissuration instables, en se basant sur les critères de la tension tangentielle maximale, de la tension principale tangentielle maximale, de la déformation tangentielle maximale et de la densité d'énergie de déformation. Les résultats présentés ici constituent un complément à ceux présentés dans la première partie de cette investigation. Certaines des prédictions théoriques ont été comparées avec des données disponibles dans la littérature.On montre que les quatre critères peuvent être appliqués de manière plus ou moins indifférente dans les cas étudiés pour prédire la direction de l'extension uniaxiale de la fissure ainsi que la charge critique. Néanmoins, les chemins de fissuration instables diffèrent selon les critères utilisés. La différence étant la plus grande dans le cas du critère de densité d'énergie de déformation. On trouve certaines difficultés à appliquer ce critère à certaines situations.

     

Modelling of Surface Crack Growth under Lubricated Rolling–Sliding Contact Loading

The paper describes modelling approach to computational simulation of surface crack growth subjected to lubricated rolling–sliding contact conditions. The model considers the size and orientation of the initial crack, normal and tangential loading due to rolling–sliding contact and the influence of fluid trapped inside the crack by a hydraulic pressure mechanism. The motion of the contact sliding load is simulated with different load cases. The strain energy density (SED) and maximum tangential stress (MTS) crack propagation criteria are modified to account for the influence of internal pressure along the crack surfaces due to trapped fluid. The developed model is used to simulate surface crack growth on a gear tooth flank, which has been also experimentally tested. It is shown that the crack growth path, determined with modified crack propagation criteria, is more accurately predicted than by using the criteria in its classical form.     

Evaluating MTS criterion in predicting mixed-mode crack extension under different loading conditions

The maximum tangential stress (MTS) criterion is one of the most widely used criteria for predicting the direction of crack extension. The suitability of this criterion is examined under different loading conditions using the extended finite element method (XFEM). Experimental and numerical results reported in the literature are considered to evaluate the validity and accuracy of the criterion. The results demonstrate that the MTS criterion evaluated by stress intensity factors (SIFs) can accurately predict the direction of crack propagation in specimens under direct tensile loading. This criterion overestimates the angle of crack initiation in the specimen under indirect tensile loading but underestimates the angle in the specimen subjected to 3-point bending. It is concluded that the MTS criterion based on SIFs could not accurately predict the direction of the crack initiation, which could, however, be determined properly based on the stress distribution around the crack tip obtained by the XFEM numerical models.     

Investigation of Mixed Mode I/II Brittle Fracture Using ASCB Specimen

Using the asymmetric semi-circular bend specimen (ASCB) with vertical crack, a series of mixed mode I/II fracture tests were performed on two different rigid polyurethanes materials. The experimental results obtained for brittle fracture are compared with the theoretical predictions based on MTS and SED criteria. The results demonstrate that the SED criterion gives better results for mode II loading conditions, while for mode I and predominantly mode I both criteria are accurate.     

A new solution for 3D crack extension based on linear elastic stress fields

A solution to the 3D stress field based on the maximum tangential stress (MTS) criterion is presented in this paper. The solution allows for the estimation of the critical crack plane, the direction of growth in terms of both twist and tilt angles and the equivalent crack driving force for a given mixed-mode loading condition. It also shows the graphical relationship between the three different stress intensities for a given driving force. Initial results have shown good correlation with experimental data obtained from literature.     

A Review of Critical Plane Orientations in Multiaxial Fatigue Failure Criteria of Metallic Materials

The paper presents a review of multiaxial fatigue failure criteria based on the critical plane concept. The criteria have been divided into three groups, according to the fatigue damage parameter used in the criterion, i.e. (i) stress, (ii) strain and (iii) strain energy density criteria. Each criterion was described mainly by the critical plane orientation. Multiaxial fatigue criteria based on the critical plane concept usually apply different loading parameters in the critical plane whose orientation is determined by (a) only shear loading parameters (crack Mode II or III), (b) only normal loading parameters (crack Mode I) or sometimes (c) mixed loading parameters (mixed crack Mode). There are also criteria based on few critical plane orientations and criteria based on critical plane orientations determined by a weighted averaging process of rotating principal stress axes.     

Mixed mode fracture analysis of CCBD specimens based on the extended maximum tangential strain criterion

The maximum tangential strain (MTSN) criterion has been modified to include the effects of T‐stress and stress intensity factors in conditions of both plane stress and plane strain. Further, both the T‐stress and Poisson's ratio affecting the crack propagation are also discussed according to the extended MTSN (EMTSN) criterion, which is a modified MTSN criterion. Finally, the generalized maximum tangential stress (GMTS) criterion and the EMTSN criterion are used to predict the test results obtained with central cracked Brazilian disc (CCBD) specimens. The results indicate that the T‐stress and Poisson's ratio have a remarkable influence on the mixed mode fracture resistance based on the EMTSN criterion. Theoretical values of both the EMTSN and the GMTS criteria are in very good agreement with the test results. Moreover, the EMTSN criterion provides a better prediction for pure mode II.     

A non-local stress and strain energy release rate mixed mode fracture initiation and propagation criteria

A non-local stress condition for crack initiation and propagation in brittle materials is presented. This condition is expressed in terms of normal and tangential traction components acting on a physical plane segment (damage zone) of specified length. Next, a non-local strain energy release rate criterion is proposed. This condition is based on the assumption that initiation or propagation of cracking occurs when the maximal value of the function of opening and sliding energy release rates reaches a critical value. The value of energy release rates is determined for finite elementary crack growth. Mixed mode conditions are considered, for which both the critical load value and the crack orientation are predicted from the non-local stress and energy criteria, which are applicable to both regular and singular stress concentrations. The effect of non-singular second order term (T_σ-stress) on the crack propagation is discussed.     

Maximum Average Tangential Stress Criterion for Prediction of the Crack Path

The concept of the average stress has been employed to propose the maximum average tangential stress (MATS) criterion for predicting the direction of fracture angle. This criterion states that a crack grows when the maximum average tangential stress in the fracture process zone ahead of the crack tip reaches its critical value and the crack growth direction coincides with the direction of the maximum average tangential stress along a constant radius around the crack tip. The tangential stress is described by the singular and non-singular (T-stress) terms in the Williams series solution. The predicted directions of fracture angle are consistent with the experimental data for the mixed mode I/II crack growth behavior of Guiting limestone.     

The formation of fine relaxation cracks along the compressive maximum shear crack

The formation of fine short relaxation cracks frequently found along the cyclically propagating 45° compressive maximum shear crack were analyzed. Comparison was made of the results computed from two different fracture criteria, the minimum strain energy density (MSED) and the maximum tensile (tangential) stress (MTS). The measured directions θ₀ of the relaxation cracks were in excellent accord with both the theoretical MSED directions and the MTS directions. The computed MSED crack directions were predicated on two conditions: 1) the strain energy density factor was minimum, S _min, and 2) the volume change component S _v of S _min was greater than the distortion component S _d. Such requirements correspond to crack directions with locally maximum tensile tangential stresses.     

脆性材料复合型裂纹的断裂准则

实际工程中,脆性材料中的裂纹多处于复合型受力状态,因此,确定脆性材料中的复合型裂纹起裂角和临界荷载有着重要的理论意义和实用价值。以复合型裂纹为研究对象,将裂纹尖端的最小无量纲塑性区尺度ρmin和广义合成偏应力强度理论相结合,建立脆性材料复合型裂纹的断裂准则,预测裂纹起裂角及临界荷载,将其结果与最大周向应力准则和应变能密度因子准则相比较发现,基于该文方法得到的临界荷载曲线大于最大周向应力准则得到的临界荷载曲线,与应变能密度因子准则得到的临界荷载曲线比较接近。因而,表明了用该文的方法来预测脆性材料复合型裂纹起裂角和临界荷载是行之有效的。     

Dual boundary element method and finite element method for mixed‐mode crack propagation simulations in a cracked hollow shaft

Three‐dimensional mixed‐mode crack propagation simulations were performed by means of the dual boundary element method code BEASY and 2 finite element method‐based crack propagation codes: ZENCRACK (ZC) and CRACKTRACER3D (CT3D). The stress intensity factors (SIFs) along the front of an initial semielliptical crack, initiated from the external surface of a shaft, were calculated for 4 different load cases: bending, press fit, shear, and torsion. The methods used for the SIF assessment along the crack front were the J‐integral for BEASY and ZC and the quarter point element stress method for CT3D. Subsequently, crack propagation simulations were performed, with the crack growth rate evaluated by using Paris' law, calibrated for the material at stake (American Society for Testing and Materials A469 steel). The kink angles were evaluated by using the minimum strain energy density and maximum tangential stress criteria for BEASY, the maximum energy release rate and maximum tangential stress for ZC, and the maximum principal asymptotic stress for CT3D. The results obtained in terms of SIFs and crack propagation life show very good agreement among the 3 codes. Also, the shape of the propagated crack, which is significantly out‐of‐plane for the shear and torsion loading, matched very well.     

Unified triaxiality at the crack tip subjected to plane strain condition under mixed‐mode (I + II) fracture

The new model of stress triaxiality, subjected to plane strain condition under mixed‐mode (I + II) loading, at the yield loci of the crack tip, has been formulated using unified strength theory. It evaluates critical values of triaxiality for various convex and non‐convex failure criteria, unlike the existing model. It shows the effects of Poisson's ratio and intermediate principal stress for materials whose strength in tension and compression is either equal or unequal. Further, on this basis, the crack initiation angles are predicted for various crack inclinations and compared with those obtained from other fracture criteria. The plastic zone shapes supplement the results. Critical yield stress factor, a significant parameter at the crack tip got lowered as the difference among the three principal stresses reduced to a minimum. The crack initiation angles obtained from the model showed good agreement with those obtained from G‐, S‐, and T‐criterion.     

Multiaxial fatigue of rubber: Part I: equivalence criteria and theoretical aspects

This paper investigates commonly used approaches for fatigue crack nucleation analysis in rubber, including maximum principal strain (or stretch), strain energy density and octahedral shear strain criteria. The ability of these traditional equivalence criteria, as well as a recent equivalence criterion (the cracking energy density) to predict multiaxial fatigue behaviour is explored. Theoretical considerations are also introduced relating to the applicability of various fatigue life analysis approaches. These include the scalar nature of traditional equivalence criteria, robustness of the criteria investigated for a wide range of multiaxial loadings, effects of crack closure and applications to non‐proportional multiaxial loadings. It is shown that the notion of a stress or strain amplitude tensor used for the analysis of multiaxial loading in metals is not appropriate in the analysis of rubber due to nonlinearity associated with finite strains and near incompressibility. Taken together, these considerations illustrate that traditional criteria are not sufficiently consistent or complete to permit confident analysis of arbitrary multiaxial loading histories, and that an analysis approach specific to the failure plane is needed. Of the three traditional criteria, maximum principal strain is shown to match most closely to the cracking energy density criterion, in terms of a failure locus in principal stretch space.     

Fatigue crack closure determination by means of finite element analysis

Plasticity-induced crack closure is an observed phenomenon during fatigue crack growth. However, accurate determination of fatigue crack closure has been a complex task for years. It has been approached by means of experimental and numerical methods. The finite element method (FEM) has been the principal numerical tool employed. In this paper the results of a broad study of fatigue crack closure in plane stress and plane strain by means of FEM are presented. The effect of three principal factors has been analysed in depth, the maximum load, the crack length and the stress ratio. It has been found that the results are independent of maximum load and the crack length, and there exists a direct influence of the stress ratio. This relation has been numerically correlated and compared with experimental results. Differences have also been established between opening and closure points and between the different criteria employed to compute crack closure.     

复合型裂纹起裂角厚度效应的实验研究

完成了飞机结构铝合金LC4CS的2、4、8和14mm四种不同厚度试样在I+II复合加载条件下的复合型断裂实验,系统分析了厚度和复合载荷对裂纹起裂角的影响,揭示了常用复合型断裂准则的厚度适用范围,用三维断裂理论对结果进行了讨论。结果表明:复合型裂纹起裂角具有明显的厚度效应;最大周向应力准则能够准确预测薄试样和厚试样(厚度为2 mm 和14 mm)在各种复合加载条件下的起裂方向,但是不适用于中间厚度的试样,尤其是8 mm厚度的情况。最大三轴应力准则试图考虑裂纹尖端三维约束对裂纹起裂的影响,但是结果并不理想。最小应变能密度因子理论的预测结果与最大周向应力准则的预测结果非常接近,但同样不能预测8mm厚度试样的起裂方向。非常有必要建立一个普遍适用的三维复合型断裂准则。     

A fracture mechanics model for the analysis of micro-pitting in regard to lubricated rolling–sliding contact problems

A computational model is presented for the analysis of micro-pitting in regard to lubricated rolling–sliding contact problems. This model assumes the appearance of an initial microcrack on the contact surface due to the mechanical or thermal treatment of the material, and as a consequence of an on-going process in early the stage of exploitation. The discretised model of the contacting mechanical elements is subjected to normal loading (Hertzian contact pressure), tangential loading (friction between contacting surfaces) and internal pressure to the crack surfaces. Crack propagation is predicted as follows: (1) using modified maximum tangential stress criterion, which takes into account the influence of stress intensity factors K_I and K_II, T-stress, stress on the crack’s surface caused by lubricant pressure inside the crack, and the critical distance ahead of the crack tip and (2) the classical maximum tangential stress criterion, which only takes into account the influence of the stress intensity factors K_I and K_II. The stress intensity factor based on these two criteria is then used in a short crack growth theory to determine the fatigue life of an initial crack to extent up to micro-pit. The developed model is applied to a real spur gear pair.     

Experimental and finite element study on stable crack growth in three point bending

Experimental and finite element results are presented on mode I and mixed mode (involving I and II only) stable crack growth under static loading through an aircraft grade aluminium alloy (D16AT) in three point bending. The results include load-displacement diagrams, J-integrals, plastic zones, tunneling (or crack front curving), etc. During experiment a substantial amount of tunneling is observed, the extent of which increases as the extension progresses in both mode I and mixed mode. The tunneling reduces as a_o/w increases. The crack extends initially almost along a straight line at an angle with the initial crack in a mixed mode. The maximum load is observed to be as high as 1.6 times the initiation load in the whole range examined. From the finite element study it is seen that, in a mixed mode, the J-integral at the onset of extension is the lowest compared with the values at the later stages. The plastic zone size grows as the stable extension progresses; the growth is approximately the maximum along the crack extension line. The direction of initial crack extension in a mixed mode can be predicted through an elastic finite element analysis and using the criterion of maximum tangential principal stress. The study also indicates that the load-displacement diagram associated with a mixed mode stable crack growth can be predicted reasonably accurately using the criterion of crack opening angle.