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本文提出了一种内时塑性理论的弹塑性本构矩阵,发展了内时切线刚度有限元算法。与文[1]相比,该法所需迭代次数显著减少,且无需采用加速因子。作为验证与应用的例子,分析了35CrNi3MoV钢自增强厚壁圆筒(内径22mm,外径55mm)在单调或脉动循环载荷下的弹塑性应变场和残余应力场。与实验的比较是在自增强压力分别为7245,7055,6789个大气压力下进行的。比较结果表明计算得到的残余应力值与文[2]中用Sachs镗孔法测得的残余应力值、计算得到的内压-外壁应变关系与实验结果等都吻合的较好。计算预言了脉动循环载荷下自增强残余应力的松弛现象。本文发展的非线性问题的算法具有数值稳定性好,收敛性好等优点,在实际中可能具有较大的应用价值。
In this paper, an elasto-plastic constitutive matrix of the inner-time plasticity theory is proposed, and the finite-element method for the tangential stiffness of inner time is developed. Compared with [1], this method requires a significant reduction in the number of iterations and does not require the use of acceleration factors. As an example of verification and application, the elastic-plastic strain field and residual stress field of a 35CrNi3MoV steel self-reinforced thick-walled cylinder (22 mm in inner diameter, 55 mm in outer diameter) under monotonic or pulsating cyclic loading were analyzed. The comparison with the experiment was conducted under autogenous pressures of 7,245, 70,565,789 atmospheric pressures. The comparison results show that the calculated residual stress values are in good agreement with the residual stress values measured by the Sachs boring method in [2], the calculated internal pressure-external wall strains, and the experimental results. The calculation predicts relaxation of self-reinforced residual stress under pulsating cyclic loading. The algorithm of nonlinear problem developed in this paper has many advantages such as good numerical stability, good convergence, etc. It may have great application value in practice.