In this paper, we present polynomial varying modified polarization saturation models for semipermeable two unequal collinear cracks with coalesced interior zones in piezoelectric media. Under the influence of far-field electromechanical loadings, the cracks situated in an infinite arbitrary polarized piezoelectric media are opened in self-similar manner, forming a strip saturated zone in front of the cracks-tips. Here, we modify the polarization saturation (PS) model in a way by arresting these zones with linear, quadratic and cubic polynomials types variable saturated conditions in place of constant saturated condition. Such modified PS models are, by using complex variable and Stroh formalism techniques, firstly reduced into simultaneous non-homogeneous Riemann–Hilbert problems in complex variable field functions, and the corresponding solutions are then obtained. The closed-form solutions for standard fracture parameters such as saturated zone lengths, local stress intensity factors(LSIFs), crack opening displacements and crack opening potentials are derived. Numerical studies are illustrated for all the modified PS models by analyzing the effects on saturated zone lengths and LSIFs with respect to the variations in electrical loadings, poling direction and crack lengths. Moreover, the obtained results are compared with the results of PS model. The study concludes that the saturated zone lengths and LSIFs increase significantly with the increase in degree of polynomial varying saturation condition.

在本文中，我们提出了在压电介质中具有合并内部区域的半渗透性两个不等共线裂纹的多项式变化修正极化饱和模型。在远场机电载荷的影响下，位于无限任意极化压电介质中的裂纹以自相似的方式张开，在裂纹尖端的前面形成了一个条状的饱和区。在这里，我们通过用线性，二次和三次多项式类型的可变饱和条件代替恒定饱和条件来阻止这些区域，从而以某种方式修改了极化饱和（PS）模型。通过使用复杂变量和Stroh形式主义技术，这种经过修改的PS模型首先被简化为复杂变量场函数中同时发生的非齐次Riemann-Hilbert问题，然后获得相应的解决方案。标准的封闭式解决方案推导了饱和区长度，局部应力强度因子（LSIFs），开裂位移和开裂电位等断裂参数。通过分析对饱和区长度和LSIF的影响（相对于电载荷，极化方向和裂纹长度的变化），对所有修改后的PS模型进行了数值研究。此外，将获得的结果与PS模型的结果进行比较。研究得出结论，随着多项式变化的饱和条件程度的增加，饱和区长度和LSIFs显着增加。