基于有限元修正法的薄膜温度本构构建及验证

Construction and Verification of Thin Film Temperature Constitutive Model Based on Finite Element Correction Method

中文关键词: 聚乙烯/尼龙/聚乙烯(PE/PA/PE)  有限元修正法  温度效应  弹塑性本构模型

英文关键词: polyethylene/nylon/polyethylene (PE/PA/PE)  finite element correction method  temperature effect  elastoplastic constitutive model

中文摘要:

      目的 由于薄膜在受力过程中易产生颈缩现象，且具有强烈的温度依赖性，现有工程应力-应变与本构模型均不能准确描述温度变化下的薄膜材料的载荷位移曲线，造成预测结果与实际严重不符，该问题亟待解决。方法 在准静态拉伸(10 mm/min)与不同温度(−20、0、20、40、60 ℃)条件下，利用万能材料试验机对PE/PA/PE薄膜试样进行单轴拉伸试验，基于有限元修正法对材料的塑性应力进行修正，采用指数函数对PE/PA/PE薄膜的弹性模量、屈服强度进行描述，针对Johnson-Cook本构模型中的形函数进行修正，结合应变-温度耦合的温度项构建PE/PA/PE薄膜100%应变下的塑性应力-应变模型，在单层PE与五层PE/PA/PE/PA/PE薄膜中进行仿真验证。结果 在−20~60 ℃下100%应变范围内薄膜颈缩从7.86 mm增加到8.12 mm;弹性模量、屈服强度与塑性应力随着温度的升高呈非线性降低;基于有限元修正法对真实应力应变进行修正并进行对比，发现相对误差由83.94%降低到4.73%;采用指数函数对弹性模量、屈服强度进行拟合，R²值分别为0.936和0.947;改进后的形函数与原模型对比，相对误差从42.5%降到6.49%;温度项与修正后的应力-应变最大相对误差为7.21%。将新构建的模型应用于PE与PE/PA/PE/PA/PE薄膜，最大相对误差为4.91%。结论 在温度−20~60 ℃内，基于有限元修正法和修正后的本构模型能够很好地描述应变在100%以内的屈服强度、弹性模量和塑性应力随温度变化的规律，研究结果为薄膜的应用奠定了理论基础。

英文摘要:

      Because the thin film is prone to necking under stress, and has strong temperature dependence, the existing engineering stress-strain and constitutive model can not accurately describe the load displacement curve of the thin film material under the temperature change, resulting in a serious inconsistency between the predicted results and the actual situation, which needs to be solved urgently. Under the conditions of quasi-static tension (10 mm/min) and different temperature (−20, 0, 20, 40, 60 ℃), the uniaxial tensile test of PE/PA/PE film samples was carried out with an universal material testing machine. The plastic stress of the material was modified based on the finite element correction method. The elastic modulus and yield strength of PE/PA/PE films were described by the exponential function, and the shape function in the Johnson cook constitutive model was modified. Combined with the temperature term of strain temperature coupling, the plastic stress-strain model of PE/PA/PE films under 100 % strain was constructed, and the simulation was carried out in single-layer PE and five-layer PE/PA/PE/PA/PE films. The necking of the film increased from 7.86 to 8.12 mm in the 100 % strain range at −20-60 ℃; The elastic modulus, yield strength and plastic stress decreased nonlinearly with the increase of temperature; Based on the finite element correction method, the real stress and strain were corrected and compared. It was found that the relative error decreased from 83.94% to 4.73%; The elastic modulus and yield strength were fitted by exponential function, and the R2 values were 0.936 and 0.947, respectively; Compared with the original model, the relative error of the improved shape function was reduced from 42.5% to 6.49%; The maximum relative error between the temperature term and the corrected stress-strain was 7.21%. The maximum relative error of the new model applied to PE and PE/PA/PE/PA/PE films was 4.91%. In the temperature range of −20-60 ℃, the modified finite element method and the modified constitutive model can well describe the variation of yield strength, elastic modulus and plastic stress with temperature when the strain is within 100 %. The research results lay a theoretical foundation for the application of thin films.