β型钛合金高温粘塑性本构建模及数值计算
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摘要
钛合金由于常温具有强烈的回弹倾向,因此常采用温间压力成形进行成形处理,但是许多钛合金在β相变点以上的应力应变曲线表现出明显的屈服点现象、急剧的屈服应力下降、应变软化以及强烈的应变速率敏感性。目前仍未有成熟的本构模型能够准确描述这一类特殊的粘塑性变形特征,因此无法对温间压力成形进行准确的模拟。
本文对β型钛合金Ti-20V-4Al-1Sn在700℃、750℃以及800℃三种温度下的单轴应力应变曲线进行了测量,对Ti-20V-4Al-1Sn在上述温度区间内不同应变速率下不同应变阶段的变形微观组织进行系统观察,分析温度、应变速率以及塑性应变对材料微观组织演化的影响。力学实验结果表明,钛合金Ti-20V-4Al-1Sn在上述温度区间内的应力应变曲线具有明显的屈服点现象、急剧的屈服应力下降、应变软化以及强烈的应变速率敏感性。微观组织分析表明,屈服点以及屈服应力下降阶段伴随着晶界处位错密度的急剧变化,在大应变阶段,动态回复是流动软化的主要原因。
基于Johnston-Gilman可动位错密度理论,本文首次推导出适用于钛合金高温粘塑性变形的本构方程,对钛合金在β相变点以上的温度区间内表现的屈服点现象、屈服点下降、流动软化以及应变速率敏感性进行建模。并采用基于多点近似拟合法的序列规划最优化方法对该粘塑性本构模型的各材料参数进行了拟合。结果表明,该本构模型能够准确的描述屈服点现象、屈服阶段的应力下降、大应变区域的流动软化以及应变速率敏感性。基于内部变量理论的本构方程构造使得该模型可以推广到其他牌号的钛合金以及表现出屈服点下降的其他材料如软钢、铝合金甚至硅晶体等。
首次基于变形的亚弹性分解理论提出大变形框架下的本构方程,利用返回图算法原理首次提出适用于屈服点现象的本构方程隐式化求解算法,推导出适用于隐式求解的单元切线刚度矩阵。最终将上述模型利用商用有限元软件MSC.MARC的子程序HYPELA2编程实现,并进行了单轴拉伸以及V型弯曲过程的计算。计算结果表明,即使在复杂的接触条件以及较大时间增量步下,有限元分析同样可以达到优良的收敛率,并准确的再现高温屈服点下降现象。
Many high temperature mechanical tests ofβtitanium alloys show a common feature that the stress-strain curves exhibit a sharp initial peak stress followed by constant flow stress or flow softening. In this paper, high temperature deformation behavior of beta titanium alloy Ti-20V-4Al-1Sn sheet is studied by performing uniaxial tension experiments at three different strain rates at high temperatures of 700°C, 750°C and 800°C. The stress-strain curves at all temperature cases show strain rate sensitivity, yield point phenomena and continuous flow softening patterns. Microstructures of deformed specimens at several representative deformation stages and different strain rates are studied using optical microscope. Dynamic recovery does not occur at the early stage of deformation including yield-point and the subsequent yield drop regime, but it is activated at large deformation stage, where it is affected by strain rate and strain.
As a first approach, a viscoplastic constitutive model based on the assumption of rapid dislocation multiplication is proposed to describe such high temperature yield-point phenomena. In this modeling, the softening effect due to dynamic recovery is also considered. The stress-strain responses predicted by the constitutive model well capture the yield-point phenomena, strain rate sensitivity and subsequent continuous flow softening behavior of the beta titanium alloy.
The constitutive model is further implemented into commercial FE code by using implicit return mapping algorithm. The numerical implementation is constructed in a corotational frame under hypoelastic hypothesis to describe large deformation behaviors. The tangent matrix is also deduced in this paper to make the numerical calculation giving excellent convergence and stable results. The FE simulation results fit well with analytical calculation even at large time step. The generality of the model and the implicit algorithm makes it possible to extend the theory to other titanium alloys and the materials that have yield-point phenomena.
本文对β型钛合金Ti-20V-4Al-1Sn在700℃、750℃以及800℃三种温度下的单轴应力应变曲线进行了测量,对Ti-20V-4Al-1Sn在上述温度区间内不同应变速率下不同应变阶段的变形微观组织进行系统观察,分析温度、应变速率以及塑性应变对材料微观组织演化的影响。力学实验结果表明,钛合金Ti-20V-4Al-1Sn在上述温度区间内的应力应变曲线具有明显的屈服点现象、急剧的屈服应力下降、应变软化以及强烈的应变速率敏感性。微观组织分析表明,屈服点以及屈服应力下降阶段伴随着晶界处位错密度的急剧变化,在大应变阶段,动态回复是流动软化的主要原因。
基于Johnston-Gilman可动位错密度理论,本文首次推导出适用于钛合金高温粘塑性变形的本构方程,对钛合金在β相变点以上的温度区间内表现的屈服点现象、屈服点下降、流动软化以及应变速率敏感性进行建模。并采用基于多点近似拟合法的序列规划最优化方法对该粘塑性本构模型的各材料参数进行了拟合。结果表明,该本构模型能够准确的描述屈服点现象、屈服阶段的应力下降、大应变区域的流动软化以及应变速率敏感性。基于内部变量理论的本构方程构造使得该模型可以推广到其他牌号的钛合金以及表现出屈服点下降的其他材料如软钢、铝合金甚至硅晶体等。
首次基于变形的亚弹性分解理论提出大变形框架下的本构方程,利用返回图算法原理首次提出适用于屈服点现象的本构方程隐式化求解算法,推导出适用于隐式求解的单元切线刚度矩阵。最终将上述模型利用商用有限元软件MSC.MARC的子程序HYPELA2编程实现,并进行了单轴拉伸以及V型弯曲过程的计算。计算结果表明,即使在复杂的接触条件以及较大时间增量步下,有限元分析同样可以达到优良的收敛率,并准确的再现高温屈服点下降现象。
Many high temperature mechanical tests ofβtitanium alloys show a common feature that the stress-strain curves exhibit a sharp initial peak stress followed by constant flow stress or flow softening. In this paper, high temperature deformation behavior of beta titanium alloy Ti-20V-4Al-1Sn sheet is studied by performing uniaxial tension experiments at three different strain rates at high temperatures of 700°C, 750°C and 800°C. The stress-strain curves at all temperature cases show strain rate sensitivity, yield point phenomena and continuous flow softening patterns. Microstructures of deformed specimens at several representative deformation stages and different strain rates are studied using optical microscope. Dynamic recovery does not occur at the early stage of deformation including yield-point and the subsequent yield drop regime, but it is activated at large deformation stage, where it is affected by strain rate and strain.
As a first approach, a viscoplastic constitutive model based on the assumption of rapid dislocation multiplication is proposed to describe such high temperature yield-point phenomena. In this modeling, the softening effect due to dynamic recovery is also considered. The stress-strain responses predicted by the constitutive model well capture the yield-point phenomena, strain rate sensitivity and subsequent continuous flow softening behavior of the beta titanium alloy.
The constitutive model is further implemented into commercial FE code by using implicit return mapping algorithm. The numerical implementation is constructed in a corotational frame under hypoelastic hypothesis to describe large deformation behaviors. The tangent matrix is also deduced in this paper to make the numerical calculation giving excellent convergence and stable results. The FE simulation results fit well with analytical calculation even at large time step. The generality of the model and the implicit algorithm makes it possible to extend the theory to other titanium alloys and the materials that have yield-point phenomena.
引文
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