A coupled stress and energy failure model for crack initiation in arbitrarily shaped adhesive lap joints

In this work, crack initiation in adhesive lap joints of arbitrary joint configuration is studied by means of a finite fracture mechanics approach. The analysis is based on a general stress solution for adhesive joints combined with a coupled stress and energy criterion. The instantaneous formation of a crack of finite size is predicted if a stress and energy criterion are satisfied simultaneously. The closed-form analytical solution of the stress field allows for an efficient evaluation of the crack initiation load and corresponding finite crack length. A comparison to experimental results from literature and to numerical results obtained with a cohesive zone model approach shows a good agreement. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Crack formation under compression

This paper presents a theoretical analysis of the formation of a tensile stress zone (separation zone) in a crack of finite width under uniaxial transverse compression, assuming the existence of prefracture zones that satisfy a linear one-parameter relationship between stress and displacement vectors. A crack formation criterion is stated, and practical fracture criteria are analyzed from the point of view of locality of the crack formation process.Simferopol' University. Translated from Dinamicheskie Sistemy, No. 10, pp. 3–8, 1992.     

双I—型裂纹断裂动力学问题的非局部理论解

研究了非局部理论双中I－型裂纹弹性波散射的力学问题,并利用富里叶变换使本问题的求解转换为三重积分方程的求解,进而采用新方法和利用一维非局部积分核代替二维非局部积分核来确定裂纹尖端的应力状态,这种方法就是Schmidt方法,所得结是比艾林根研究断裂静力学问题的结果准确和更加合理,克服了艾林根研究断裂静力学问题时遇到的数学困难,与经典弹性解相比,裂纹尖端不再出现物理意义下不合理的应力奇异性,并能够解释宏观裂纹与微观裂纹的力学问题。     

Assessment of asymmetric crack initiation in open-hole plates using a coupled stress and energy criterion

An application of the finite fracture mechanics concept to open-hole plates subject to combined tensile and bending loading is presented. In finite fracture mechanics, the simultaneous satisfaction of both, a stress and an energy criterion, is enforced as a condition for crack initiation. Efficient modeling and closed-form expressions for the dependence of the stress and energy quantities on governing structural and material parameters allow for a comprehensive numerical analysis of the onset of asymmetric crack patterns. The obtained failure load predictions are found to agree well with a cohesive zone model and experimental data from literature. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Non-local theory solution of two collinear mode-I cracks in piezoelectric materials

In this paper, the basic solution of two collinear cracks in a piezoelectric material plane subjected to a uniform tension loading is investigated by means of the non-local theory. Through the Fourier transform, the problem is solved with the help of two pairs of integral equations, in which the unknown variables are the jumps of displacements across the crack surfaces. To solve the integral equations, the jumps of displacements across the crack surfaces are directly expanded in a series of Jacobi polynomials. Numerical examples are provided to show the effects of the interaction of two cracks, the materials constants and the lattice parameter on the stress field and the electric displacement field near crack tips. Unlike the classical elasticity solution, it is found that no stress and electric displacement singularities are present at crack tips. The non-local elastic solutions yield a finite hoop stress at the crack tip, thus allowing us to using the maximum stress as a fracture criterion in piezoelectric materials.     

采用新方法研究非局部理论中Ⅰ-型裂纹的断裂问题

采用新的方法研究非局部理论中Ⅰ_型裂纹的断裂问题,进而确定裂纹尖端的应力状态,这种方法就是Schmidt方法·　所得结果比艾林根研究同样问题的结果准确和更加合理,克服了艾林根研究同样问题时遇到的数学困难·　与经典弹性解相比,裂纹尖端不再出现物理意义上不合理的应力奇异性,并能够解释宏观裂纹与微观裂纹的力学问题·     

幂律非线性粘弹性材料中的裂纹扩展*

对蠕变不可压幂律非线性粘弹性材料中裂纹的蠕变扩展进行了分析,为描述银纹带中的力学行为,假设在裂纹尖端邻域中断裂过程区中分布着阻抗裂纹张开的粘聚应力б_f,.通过对均匀应力参考状态平凡解的摄动,将非线性粘弹性问题化成线性问题处理.对于幂指数.n≌1的弱非线性情况得到了应力与位移表达式.提出断裂过程区局域能量判据,导出了裂纹孕育时间t*与蠕变扩展率a的预测公式.     

The onset of mixed-mode intralaminar cracking in a cross-ply composite laminate

The intralaminar fracture toughness of a unidirectionally reinforced glass/epoxy composite is determined experimentally at several mode I and mode II loading ratios. The crack propagation criterion, expressed as a quadratic form in terms of single-mode stress intensity factors (alternatively, linear in terms of energy release rates), approximates the test results reasonably well. The mixed-mode cracking criterion obtained is used to predict the intralaminar crack on set in a cross-ply glass/epoxy composite under off-axis tensile loading. Translated from Mekhanika Kompozitnykh Materialov, Vol. 44, No. 6, pp. 785–794, November–December, 2008.     

Effect of Coulomb friction on the fiber/matrix debonding and matrix cracking in unidirectional fiber-reinforced brittle-matrix composites

A model for a macroscopic crack transverse to bridging fibers is developed based upon the Coulomb friction law, instead of the hypothesis of a constant frictional shear stress usually assumed in fiber/matrix debonding and matrix cracking analyses. The Lamé formulation, together with the Coulomb friction law, is adopted to determine the elastic states of fiber/matrix stress transfer through a frictionally constrained interface in the debonded region, and a modified shear lag model is used to evaluate the elastic responses in the bonded region. By treating the debonding process as a particular problem of crack propagation along the interface, the fracture mechanics approach is adopted to formulate a debonding criterion allowing one to determine the debonding length. By using the energy balance approach, the critical stress for propagating a semi-infinite fiber-bridged crack in a unidirectional fiber-reinforced composite is formulated in terms of friction coefficient and debonding toughness. The critical stress for matrix cracking and the corresponding stress distributions calculated by the present Coulomb friction model is compared with those predicted by the models of constant frictional shear stress. The effect of Poisson contraction caused by the stress re distribution between the fiber and matrix on the matrix cracking mechanics is shown and discussed in the present analysis. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 43, No. 2, pp. 171–190, March–April, 2007.     

Shape sensitivity of a plane crack front

The 3D‐elasticity model of a solid with a plane crack under the stress‐free boundary conditions at the crack is considered. We investigate variations of a solution and of energy functionals with respect to perturbations of the crack front in the plane. The corresponding expansions at least up to the second‐order terms are obtained. The strong derivatives of the solution are constructed as an iterative solution of the same elasticity problem with specified right‐hand sides. Using the expansion of the potential and surface energy, we consider an approximate quadratic form for local shape optimization of the crack front defined by the Griffith criterion. To specify its properties, a procedure of discrete optimization is proposed, which reduces to a matrix variational inequality. At least for a small load we prove its solvability and find a quasi‐static model of the crack growth depending on the loading parameter. Copyright © 2003 John Wiley & Sons, Ltd.     

Approximate methods for analyzing the growth of large cracks in fatigue damaged aircraft sheet material and lap joints

Several levels of approximation are investigated to account for the effect of small fatigue cracks on the residual strength of aircraft sheet materials and fuselage lap joints containing major cracks. A version of the Dugdale model is proposed which accounts for strain hardening of the sheet in an approximate way and which incorporates a criterion for crack advance leading to crack growth resistance. This model builds upon the model proposed by Nilsson and Hutchinson [1] and accounts for the detailed interaction between the major crack and the small damage cracks. A simpler version of the model uses the damage-reduced local strength of the sheet or joint in assessing the effect of the major crack on residual strength. The simpler approach thus bypasses the necessity of a direct determination of the highly complicated details of the interaction of the small cracks in a lap joint with a major crack.     

Crack nucleation sensitivity analysis

A simple analytical expression for crack nucleation sensitivity analysis is proposed relying on the concept of topological derivative and applied within a two‐dimensional linear elastic fracture mechanics theory (LEFM). In particular, the topological asymptotic expansion of the total potential energy together with a Griffith‐type energy of an elastic cracked body is calculated. As a main result, we derive a crack nucleation criterion based on the topological derivative and a criterion for determining the direction of crack growth based on the topological gradient. The proposed methodology leads to an axiomatic approach of crack nucleation sensitivity analysis. Copyright © 2010 John Wiley & Sons, Ltd.     

Investigation of the local behavior of different cohesive zone models

Cohesive interface elements are well suited for three-dimensional crack propagation analyses as long as the crack path is known. This is the case e.g. in delamination analyses of laminated composite structures or failure analyses of adhesively bonded joints. Actually, they are widely used in such applications for both brittle and ductile systems. As long as the strength and fracture toughness of the material are accurately captured it is generally accepted that the shape of the cohesive law has little to no influence on the mechanical behavior of the investigated structures. However, when having a look on the local behavior of different cohesive zone models, such as stress distribution in the fracture process zone, the results exhibit certain differences. These will be studied in the present contribution. Especially the local stress distribution will be investigated and the effect on the computational efficiency will be pointed out. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical simulation of the non‐linear crack problem with non‐penetration

Here the numerical simulation of some plane Lamé problem with a rectilinear crack under non‐penetration condition is presented. The corresponding solids are assumed to be isotropic and homogeneous as well as bonded. The non‐linear crack problem is formulated as a variational inequality. We use penalty iteration and the finite‐element method to calculate numerically its approximate solution. Applying analytic formulas obtained from shape sensitivity analysis, we calculate then energetic and stress characteristics of the solution, and describe the quasistatic propagation of the crack under linear loading. The results are presented in comparison with the classical, linear crack problem, when interpenetration between the crack faces may occur. Copyright © 2004 John Wiley & Sons, Ltd.     

Derivatives of the energy functional for 2D‐problems with a crack under Signorini and friction conditions

We consider the two‐dimensional elasticity problem for an elastic body with a crack under unilateral constraints imposed at the crack. We assume that both the Signorini condition for non‐penetration of the crack faces and the condition of given friction between them are fulfilled. The problem is non‐linear and can be described by a variational inequality. Varying the shape of the crack by a local coordinate transformation of the domain, the first derivative of the energy functional to the problem with respect to the crack length is obtained, which gives the criterion for the crack growing. The regularity of the solution is discussed and the singular solution is performed. Copyright © 2000 John Wiley & Sons, Ltd.     

Conditions for Cracking and Debond Development at Partially Bonded Bimaterial Half-Planes

Fracture phenomena at the debond tip of partially bonded bimaterial half-planes subjected to concentrated normal forces, couples, and uniform tension are considered. The crack initiation conditions are described by the stress distribution before the initiation and the energy release rate of the crack immediately after the initiation. The debond development conditions are described by the stress distribution and the energy release rate of the debond before its initiation. When both the crack and the debond have chances to occur, or when cracks can arise in both the materials, the fracture phenomena are predicted by comparing the ratio of energy release rates and the ratio of fracture toughnesses.     

Shape sensitivity of curvilinear cracks on interface to non-linear perturbations

The 2D-model of an anisotropic, non-homogeneous, bonded elastic solid with a crack on the interface is considered. We state the linear problem with the stress-free boundary condition at the crack faces in addition to the transmission condition at the connected part of the interface. The sensitivity of the model to non-linear perturbations of the curvilinear crack along the interface is investigated. We obtain the asymptotic expansion and the corresponding derivatives of the potential energy functional with respect to the crack length via the material derivatives of the solution. This allows us to describe the growth or stationarity, and the local optimality conditions by the Griffith rupture criterion. The integral expression of the energy release rate for the considered problems is obtained, and the Cherepanov-Rice integral is discussed.     

From finite to linear elastic fracture mechanics by scaling

In the setting of finite elasticity we study the asymptotic behaviour of a crack that propagates quasi-statically in a brittle material. With a natural scaling of size and boundary conditions we prove that for large domains the evolution with finite elasticity converges to the evolution with linearized elasticity. In the proof the crucial step is the (locally uniform) convergence of the non-linear to the linear energy release rate, which follows from the combination of several ingredients: the \(\Gamma \) -convergence of re-scaled energies, the strong convergence of minimizers, the Euler–Lagrange equation for non-linear elasticity and the volume integral representation of the energy release.     

Interface cracks in anisotropic composites

The linear model equations of elasticity often give rise to oscillatory solutions in some vicinity of interface crack fronts. In this paper we apply the Wiener–Hopf method which yields the asymptotic behaviour of the elastic fields and, in addition, criteria to prevent oscillatory solutions. The exponents of the asymptotic expansions are found as eigenvalues of the symbol of corresponding boundary pseudodifferential equations. The method works for three‐dimensional anisotropic bodies and we demonstrate it for the example of two anisotropic bodies, one of which is bounded and the other one is its exterior complement. The common boundary is a smooth surface. On one part of this surface, called the interface, the bodies are bonded, while on the complementary part there is a crack. By applying the potential method, the problem is reduced to an equivalent system of Boundary Pseudodifferential Equations (BPE) on the interface with the stress vector as the unknown. The BPEs are defined via Poincaré–Steklov operators. We prove the unique solvability of these BPEs and obtain the full asymptotic expansion of the solution near the crack front. As a special case we consider the interface crack between two different isotropic materials and derive an explicit criterion which prevents oscillatory solutions. Copyright © 1999 John Wiley & Sons, Ltd.     

论复合型脆断的周向应变因子准则

本文讨论了线弹性断裂力学的复合型断裂准则.推荐了周向应变因子准则.