Fracture of the adhesive layer (AL) of finite thickness with elastoplastic properties in a layered composite is considered in this article. The expression of the $${J}_{C}$$ -integral is obtained as the sum of values of the products of the layer thickness and the increments of the specific free energy and specific dissipation. Based on the variational formulation, a solution to the model problem of shear action on a thin elastoplastic layer is obtained. From the analysis of the solution obtained, it follows that in the case of a layer degenerating into a mathematical section, the main contribution to the representation of the $${J}_{C}$$ -integral is made by the term responsible for the energy dissipation, and the energy product tends to zero. In this case, it is not pure dissipation that is considered, this is the product of specific dissipation and layer thickness. The expression of the $${J}_{C}$$ -integral is obtained in terms of the quantities measured in a possible experiment.

中文翻译：

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$${J}_{c}$$与层状复合材料胶层耗散能的关系

本文考虑了层状复合材料中具有弹塑性的有限厚度粘合剂层 (AL) 的断裂。$${J}_{C}$$ - 积分的表达式作为层厚度与特定自由能和特定耗散的增量的乘积值的总和获得。基于变分公式，得到了薄弹塑性层上剪切作用模型问题的解。从对所获得的解决方案的分析来看，在层退化为数学部分的情况下，对 $${J}_{C}$$ - 积分表示的主要贡献是由术语负责为能量耗散，能量积趋于零。在这种情况下，考虑的不是纯耗散，这是特定耗散和层厚度的乘积。$${J}_{C}$$ - 积分的表达式是根据可能实验中测量的数量获得的。