Fracture and debonding of a thin film on a stiff substrate: analytical and numerical solutions of a one-dimensional variational model
Fracture and debonding of a thin film on a stiff substrate: analytical and numerical solutions of a one-dimensional variational model
复制标题
刚性基底上薄膜的断裂和脱粘：一维变分模型的解析和数值解
DOI：
10.1007/s00161-012-0245-x
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发表时间：
2013
影响因子：
2.6
通讯作者：
C. Maurini
中科院分区：
文献类型：
--
作者：
Andrés A. León Baldelli;B. Bourdin;J. Marigo;C. Maurini
本文用断裂力学的变分方法研究了与刚性基体结合的薄膜的多裂和脱粘现象。我们考虑一个简化的一维膜模型，其中载荷是通过膜中的均匀非弹性（例如，热）应变或基材的施加位移引入的。断裂现象采用Griffith模型来解释剥离和横向断裂。基于能量最小化的论点，我们恢复了实验证据的关键定性性质，如横向裂纹的周期性和每个规则段的外围剥离。相图关系到在剥离发生之前可能产生的横向裂纹的最大数量，作为材料特性和样品几何形状的函数。通过有限元离散化和Ambrosio-Tortorelli型正则变分公式得到的数值模拟说明了理论结果，该公式适合在二维环境中进一步推广。
We study multi-fissuration and debonding phenomena of a thin film bonded to a stiff substrate using the variational approach to fracture mechanics. We consider a reduced one-dimensional membrane model where the loading is introduced through uniform inelastic (e.g., thermal) strains in the film or imposed displacements of the substrate. Fracture phenomena are accounted for by adopting a Griffith model for debonding and transverse fracture. On the basis of energy minimization arguments, we recover the key qualitative properties of the experimental evidences, like the periodicity of transverse cracks and the peripheral debonding of each regular segment. Phase diagrams relate the maximum number of transverse cracks that may be created before debonding takes place, as a function of the material properties and the sample’s geometry. The theoretical results are illustrated with numerical simulations obtained through a finite element discretization and a regularized variational formulation of the Ambrosio–Tortorelli type, which is suited to further extensions in two-dimensional settings.