The main objective of this study is to determine the image forces during the interaction between the dislocation and a semi-infinite crack in a bi-material. Our problem is formulated by using two materials bonded together with an adhesive cracked at the end and loaded by an uniformly distributed load according to the first mode of fracture (Mode I). The analysis of the image forces is mainly based on the stress field generated during the cracking of the material. The study is started by taking into account a dislocation of circular form. The second step is devoted to studying the interaction between an arbitrary dislocation and a semi-infinite crack. The numerical study is treated by FEM considering a model of a flat element having a macro-crack and a dislocation, subjected to a tensile load according to the mode I. The results show that the image forces are only generated by the presence of the dislocation and are symmetrically amplified and reduced according to the position of this dislocation with respect to the semi-infinite crack. So, the orientation of the arbitrary dislocation around the semi-infinite crack generates symmetrically a positive and a negative image forces which accelerate or delay the propagation of the semi-infinite crack. Theoretical results will be compared with those found numerically.

这项研究的主要目的是确定位错与双材料中的半无限裂纹之间相互作用时的像力。我们的问题是通过使用两种材料粘合在一起而形成的，该两种材料的末端开裂并根据第一断裂方式（方式I）通过均匀分布的载荷加载。镜像力的分析主要基于材料开裂过程中产生的应力场。该研究是从考虑圆形形式的错位开始的。第二步致力于研究任意位错和半无限裂纹之间的相互作用。通过有限元法对数值研究进行了处理，考虑了具有宏观裂纹和位错的扁平元件的模型，并根据模式I对其施加了拉力载荷。结果表明，像力仅由位错的存在产生，并且根据该位错相对于半无限裂纹的位置对称地放大和减小。因此，围绕半无限裂纹的任意位错的取向对称地产生正像力和负像力，其加速或延迟半无限裂纹的传播。理论结果将与数值发现的结果进行比较。围绕半无限裂纹的任意位错的取向会对称地产生正像力和负像力，从而加速或延迟半无限裂纹的传播。理论结果将与数值发现的结果进行比较。围绕半无限裂纹的任意位错的取向对称地产生正像力和负像力，从而加速或延迟半无限裂纹的传播。理论结果将与数值发现的结果进行比较。