屈服准则、失效准则、硬化准则、速率

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0)为什么讨论这些基本问题

有限元技术发展到今天，其算法基本上已经成熟。对从事有限元软件开发的人员而言，主要的工作就是根据新材料的发展不断补充各种材料模型，不断完善材料库，同时也不断完善单元库；而对有限元使用人员来说，主要的工作就是建立几何模型，选择合适的材料及单元，设置求解参数。选择单元及设置求解参数主要牵涉到有限元基本算法，通过集中的学习可以较快的掌握；而材料模型种类繁杂，有时候并不容易选择，有必要群策群力，共同学习。

我先抛砖引玉，真诚希望大家能把这些工作做起来。为容易理解计，尽量避免使用特别专业的词汇。

(1)屈服

对许多延展性较好的材料（如大多数金属）而言，其弹性和非弹性行为一般用屈服强度（yield strength)这个标量来区分、界定。在ANSYS里，屈服点（yield point)和比例极限(proportional limit)被假定为是一致的。应力分量的组合千变万化，不可能对每个应力状态都指定屈服强度，屈服准则的作用就是将林林总总的多向应力转化为单向应力（屈服强度一般通过单向拉伸试验来测定，因为这个实验最简单。），然后将转化后的等效应力和屈服强度进行比较。在ANSYS里，主要有von Mises 和 Hilll（可以通过TB,HILL指定Hill Potential)两类准则。当然一些塑性模型有自己特殊的屈服准则，如Drucker-Prager 。

失效指材料失去承载能力或者不能满足规定的使用要求（如过大的变形等），对脆性材料，失效一般表现为断裂，对延展性材料，失效的表现形式可以是最后的断裂，或者是产生永久变形，或过大的变形等等。

ANSYS6.0以后，FC系列命令可以用来为所有的单元指定失效准则，如最大主应力，最大主应变，蔡-吴准则等等，和TB,FAIL命令有些类似。对复合材料单元（如SHELL91/99，SOLID46/191)也可以用TB,FAIL指定失效；对混凝土（SOLID65)，可以使用TB,CONCR指定裂纹的产生条件。

对各向同性材料，可以指定最大主应力，最大主应变，最大剪应力，最大Mises应力为失效应力。对各项异性材料或正交各项异性材料，通常采用最大应力或最大应变准则。应用FC命令指定最大拉伸应力和最大压应力，如果不指定后者，其缺省值与前者相同。剪应力或剪应变也应通过FC输入。蔡-吴准则也是通过FC指定。对拉压强度不同的材料（如铸铁），可以通过TB,HILL或TB,ANISO指定失效条件。FC对应的菜单路径是Main Menu > General Postproc > Failure Criteria。

必须指出的是，在ANSYS里，失效单元并不从计算中删除，因此，FC命令位于后处理中，它只是被用来从设计者的角度来衡量已建立的模型。所以，最大应力（应变）可能可能大于失效条件中指定的应力（应变）。



-- 作者：paradiseboy
-- 发布时间：2004-8-7 17:14:44

--

为了将失效的单元去除，一般要应用单元的‘生死技术。当然在ls-dyna里就很简单了。

下面的例子是杀死总应变超过许用值的单元：

/SOLU !进入求解器

...

... !标准的求解过程

SOLVE

FINISH

!

/POST1 !进入POST1

SET,...

ETABLE,STRAIN,EPTO,EQV !将总应变存入ETABLE

ESEL,S,ETAB,STRAIN,0.20 !选择所有总应变大于或等于0.20的单元

FINISH

!

/SOLU !重新进入求解器

ANTYPE,,REST

EKILL,ALL !杀死选择（超过允许值）的单元

ESEL,ALL !读入所有单元

...

... !继续求解

请参阅ETABLE,ESEL,ANTYPE和EKILL命令得到更详细的解释。




等向强化：弹性区域等向扩大（如右上图所示）

随动强化：弹性区域等大

Isotropic hardening can be used for large-strain analyses of metals (> 5-10% true strain).

Isotropic hardening is not meant for cyclic loading applications because it does not account for the

Bauschinger effect. Moreover, applicability of isotropic hardening for non-proportional loading is

left up to the user, although, generally speaking, it is meant for proportional loading only.2

On the other hand, kinematic hardening is usually meant for non-proportional, cyclic loading

since the Bauschinger effect is approximated with this model. However, it is generally meant for

small-strain applications.

Combined hardening (and Chaboche nonlinear kinematic hardening), though not discussed in

detail in this memo, can be utilized to model complex, large-strain cyclic behavior such as cyclic

hardening/softening and rachetting/shakedown.



-- 作者：paradiseboy
-- 发布时间：2004-8-7 17:17:32

--

The bilinear kinematic hardening model (BKIN) usually cannot represent large-strain effects well because of the constant tangent modulus. The true stress-strain slope of most metals usually changes as the strains increase, but the bilinear model fails to account for this due to its simple

representation. This means that the yield surface can translate forever in principal stress space, even allowing for the unrealistic possibility of passing through the origin.

There are two multilinear kinematic hardening models available in ANSYS, namely MKIN and KINH. Both models use the sublayer model, which can be thought of as a weighted response of multiple elasto-perfectly-plastic ‘layers.’ A simplified view of this is that, as a layer ‘yields,’ it becomes perfectly plastic, so it provides no stiffness response; this allows for the modeling of a piecewise linear curve. The author recommends using KINH over MKIN due to the following reasons:

? KINH allows up to 20 points per stress-strain curve, whereas MKIN only allows up to 5 points.

? For KINH, input is done via TBPT commands, which is more consistent with other piecewiselinear models such as MISO and MELAS, but MKIN relies on TBDATA input.

? KINH allows up to 40 temperature-dependent curves, whereas MKIN allows only 5 temperature-dependent curves. Furthermore, in the case of temperature-dependent curves,MKIN requires each curve to have the same strain values, whereas KINH does not.KINH is the same as MKIN with TBOPT=2, or use of Rice’s model for temperature-dependency.

As a result, KINH behaves the same as MKIN (TBOPT=2), so, due to the reasons mentioned above, the user should consider using KINH.

kiddy

好啊！希望大家都能把自己的学习心得介绍介绍，给我们这些菜鸟抛砖引玉，谢谢！