两种各向同性不同材料界面处共线裂纹平面周期阵列的有效弹簧刚度
Effective Spring Stiffness for a Planar Periodic Array of Collinear Cracks at an Interface between Two Dissimilar Isotropic Materials.
作者信息
Lekesiz Huseyin, Katsube Noriko, Rokhlin Stanislav I, Seghi Robert R
机构信息
Dept. of Mechanical Engineering, The Ohio State University, Columbus OH 43210.
出版信息
Mech Mater. 2011 Feb;43(2):87-98. doi: 10.1016/j.mechmat.2010.12.004.
Explicit analytical expressions are obtained for the longitudinal and transverse effective spring stiffnesses of a planar periodic array of collinear cracks at the interface between two dissimilar isotropic materials; they are shown to be identical in a general case of elastic dissimilarity (the well-known open interface crack model is employed for the solution). Since the interfacial spring stiffness can be experimentally determined from ultrasound reflection and transmission analysis, the proposed expressions can be useful in estimating the percentage of disbond area between two dissimilar materials, which is directly related to the residual strength of the interface. The effects of elastic dissimilarity, crack density and crack interaction on the effective spring stiffness are clearly represented in the solution. It is shown that in general the crack interaction weakly depends on material dissimilarity and, for most practical cases, the crack interaction is nearly the same as that for crack arrays between identical solids. This allows approximate factorization of the effective spring stiffness for an array of cracks between dissimilar materials in terms of an elastic dissimilarity factor and two factors obtained for cracks in a homogeneous material: the effective spring stiffness for non-interacting (independent) cracks and the crack interaction factor. In order to avoid the effect of the crack surface interpenetration zones on the effective spring stiffness, the range of the tensile to transverse load ratios is obtained under the assumption of small-scale contact conditions. Since real cracks are often slightly open (due to prior loading history and plastic deformation), it is demonstrated that for ultrasound applications the results obtained are valid for most practical cases of small interfacial cracks as long as the mid-crack opening normalized by the crack length is at least in the order of 10.
得到了两种不同各向同性材料界面处共线裂纹平面周期阵列的纵向和横向有效弹簧刚度的显式解析表达式；在一般弹性不相似情况下（求解采用著名的开放界面裂纹模型），它们被证明是相同的。由于界面弹簧刚度可通过超声反射和透射分析实验确定，所提出的表达式可用于估计两种不同材料之间脱粘面积的百分比，这与界面的残余强度直接相关。解中清楚地体现了弹性不相似、裂纹密度和裂纹相互作用对有效弹簧刚度的影响。结果表明，一般来说裂纹相互作用对材料不相似性的依赖较弱，对于大多数实际情况，裂纹相互作用与相同固体之间裂纹阵列的情况几乎相同。这使得可以根据弹性不相似因子以及从均匀材料中裂纹得到的两个因子（非相互作用（独立）裂纹的有效弹簧刚度和裂纹相互作用因子）对不同材料之间裂纹阵列的有效弹簧刚度进行近似因式分解。为了避免裂纹表面相互穿透区域对有效弹簧刚度的影响，在小尺度接触条件假设下得到了拉伸与横向载荷比的范围。由于实际裂纹通常会稍微张开（由于先前的加载历史和塑性变形），结果表明，对于超声应用，只要裂纹长度归一化的裂纹中部张开至少为10的量级，所得到的结果对于大多数小界面裂纹的实际情况都是有效的。
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