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首页> 外文期刊>Revue de Metallurgie >Modelisation du fluage anisotherme des alliages a memoire de forme a base de cuivre
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Modelisation du fluage anisotherme des alliages a memoire de forme a base de cuivre

机译：铜基形状记忆合金的等温蠕变建模

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Significant progresses were made these last years on the micromechanical modelling of the behaviour of Shape Memory Alloys (SMA). In spite of that, significant problems still remain without answer. For example, for copper-based alloys, the superelastic effect modelling gives numerical results very close to the experimental results. Contrary, the modelling of the anisothermal creep at low stress level (in particular for stress lower than 100 MPa) does not give satisfactory results. The more the applied stress is weak, the more the number of activated variants is high. These variants gather around certain privileged poles to form groups known as accommodating groups composed of four variants. The problem of the anisothermal creep at low stress level exists in the phenomenological approaches and in the micro-macro formulations. We thus propose a new formulation which takes into account the microstructure really observed during such a cooling : involving a high number of activated variants by the introduction of the concept of group of variants. The principal idea of this new approach is to consider either individual variants but groups of variants. If one considers all the possible groups composed of two variants, one obtains 300 groups. However one will consider only the groups composed of two compatible variants given by the classical interaction matrix. Thus the number of groups passes from 300 to 132. This new formulation thus leads us to propose a new matrix of interaction 132*132 between groups of variants. The first stage was to build this interaction matrix using these groups of variants, by minimizing the interaction energy between each group. 576 new compatible solutions appear in this matrix. For example, the group com- posed of variants 1 and 2 and the group composed of 7 and 8 are compatible. The cluster of 4 variants (1,2, 7 and 8) is a new compatible solution while the variants 1 and 8 (respectively 2 and 7) are incompatible in the classical interaction matrix. This step is necessary but not sufficient. Indeed, the stress are maintained constant during all the cooling phase of the crystal. In this case, the same variant is selected at strong and low stress level, and this approach considers that the applied stress is perfectly uniform in the crystal. This assumption is too restrictive and neglects the weak fluctuations of stress related to the presence of heterogeneity in the crystal. One introduces a weak fluctuation Δσ of the applied stress to take account of this phenomenon. One defines too a fluctuation ΔD~(maxi) of maximum dissipation corresponding to the fluctuation of stress. At high stress, only one variant produces dissipation ranging between D~(maxi) and (D~(maxi) - ΔD~(maxi)). When the stress decreases, a number growing of solutions potentially active have a dissipation ranging between D~(maxi) and (D~(maxi) - ΔD~(maxi)). All these solutions produce an equivalent dissipation. Among these solutions, the one with the weakest dissipation is selected. This approach makes possible to reproduce, in a very satisfactory way, the observed behaviour on a monocrystal by introducing a very reasonable value of 2 MPa for the fluctuation of the stress. This work is a contribution to the modelling of the single-crystal SMA behaviour. It makes possible to take into account the experimentally observed Magge effect in the case of the monocrystals SMA. The simultaneous use of an interaction matrix, ready to consider the interactions between groups of variants, and of a selection criterion of the variants, taking account of the fluctuations of the applied stress inside the considered crystal, are likely to simulate the observed behaviour.
机译：近年来，在形状记忆合金（SMA）行为的微机械建模方面取得了重大进展。尽管如此，仍然存在许多重大问题没有答案。例如，对于铜基合金，超弹性效应模型给出的数值结果与实验结果非常接近。相反，在低应力水平（特别是对于低于100 MPa的应力）下，等温蠕变的建模不能给出令人满意的结果。施加的应力越弱，激活的变体的数量就越多。这些变体聚集在某些特权极周围，以形成由四个变体组成的容纳组。在低应力水平下的等温蠕变问题存在于现象学方法和微观宏观配方中。因此，我们提出了一种新的配方，该配方考虑了在冷却过程中实际观察到的微观结构：通过引入变体组的概念，涉及大量活化的变体。这种新方法的主要思想是考虑单个变体，但考虑变体组。如果一个人考虑了由两个变体组成的所有可能的组，则一个人将获得300个组。但是，将仅考虑由经典交互矩阵给出的两个兼容变体组成的组。因此，组的数量从300变为132。因此，这种新的表述使我们提出了变体组之间相互作用的新矩阵132 * 132。第一步是通过最小化每组之间的交互能量，使用这些变体组构建此交互矩阵。 576个新的兼容解决方案出现在此矩阵中。例如，由变体1和2组成的组与由7和8组成的组是兼容的。 4个变体（1、2、7和8）的群集是一个新的兼容解决方案，而变体1和8（分别是2和7）在经典交互矩阵中不兼容。此步骤是必要的，但还不够。实际上，在晶体的所有冷却阶段应力都保持恒定。在这种情况下，在高应力水平和低应力水平下选择相同的变体，这种方法认为所施加的应力在晶体中是完全均匀的。该假设过于严格，忽略了与晶体中异质性有关的应力的微弱波动。考虑到这一现象，人们引入了施加应力的微弱波动Δσ。人们也定义了与应力的波动相对应的最大耗散的波动ΔD〜（maxi）。在高应力下，只有一个变体产生的耗散范围在D〜（maxi）和（D〜（maxi）-ΔD〜（maxi））之间。当应力降低时，潜在激活的溶液数量的增加具有在D〜（maxi）和（D〜（maxi）-ΔD〜（maxi））之间的耗散范围。所有这些解决方案都会产生等效的耗散。在这些解决方案中，选择了最弱的一种。通过引入非常合理的2 MPa应力波动值，该方法可以以非常令人满意的方式在单晶上再现观察到的行为。这项工作有助于对单晶SMA行为的建模。在单晶SMA的情况下，有可能考虑到实验观察到的Magge效应。考虑到所考虑的晶体内部所施加应力的波动，同时使用相互作用矩阵（准备考虑变量组之间的相互作用）和变量选择标准的同时使用，可能会模拟观察到的行为。

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