JP5521161B2 - A phase transformation behavior measurement method considering the accommodation behavior of polycrystalline shape memory alloys. - Google Patents

Description

  The present invention relates to a method for measuring a phase transformation behavior in consideration of the accommodation behavior of a polycrystalline shape memory alloy.

In order to accurately predict the phase transformation behavior of shape memory alloys, it is necessary to accurately describe that the phase transformation behavior occurs under the accommodation mechanism. Several techniques have been proposed for predicting stress / strain behavior accompanying phase transformation of shape memory alloys, but none of them describe the accommodation behavior in phase transformation accurately. Is incomplete.

Tokuda et al., Transactions of the Japan Society of Mechanical Engineers, A, 98-1000 (1999), 491-497. Panico, M., Brinson L. C., J Mechanics and Physics of Solids, 55 (2007), 2491-2511.

Polycrystalline shape memory alloys are aggregates of single crystal alloys with different crystal orientations, and each crystal grain has 24 transformation orientations. For example, if a transformation occurs in one transformation orientation of a crystal, the transformation strain produced creates internal stress that resists transformation of that transformation orientation, and the next transformation occurs in another orientation of another crystal grain. . These mechanisms work one after another to minimize the internal stress in the polycrystal during the transformation process.

The transformation strain generation process by this mechanism is called accommodation, and the mechanism that causes accommodation is called accommodation mechanism. The present invention relates to a technology that makes it possible to accurately calculate the behavior of transformation strain generated under this mechanism, that is, the accommodation behavior of transformation strain.

The technical conditions characterized by the present invention are as follows.
A polycrystalline shape memory alloy is shown by parallel connection of grains with different crystal orientations, and each grain is further divided into sub-elements. The average transformation strain of the sub-elements is taken as the transformation strain of the crystal grains. From this, the elastic strain and stress of the grains are obtained, and the decomposition shear stress at each transformation surface of each grain is obtained. When the maximum shear stress satisfies the transformation condition, the transformation strain is given to the subelement and the value of the transformation strain is calculated. , Update the elastic strain using the updated transformation strain value, update the microstress value using this elastic strain, convert the microstress to the macrostress in the macro coordinate, Considering the accommodation behavior of polycrystalline shape memory alloy, which is characterized by averaging this stress over the material structure including the subelements and making this a macro stress Phase transformation behavior measurement methods.

Given the external strain increment, calculate the stress of each grain, calculate the transformation strain if the transformation condition is satisfied, and calculate the stress redistribution due to the occurrence of transformation strain. The average stress of each crystal grain is the stress of the entire microscopic material. In this way, the stress / strain relationship of the shape memory alloy considering the transformation is obtained. In addition, the stress-strain relationship considering the effect of temperature change can be obtained by giving the temperature increment and calculating the accompanying transformation strain.

It is a model diagram of a material that exhibits accommodation behavior. This is a model diagram of the material with subelements written. It is the figure which showed the flow of calculation. It is a calculation example of the superelastic behavior of a shape memory alloy.

The form for implementing this invention is demonstrated below.
The relation between stress and strain of material is called constitutive equation. The physical model of the material used to derive this constitutive equation is called the constitutive equation model. The physical model is not a precise representation of all the behavior of the material, but is a simplified model that can reasonably represent the required material response and is necessary to formulate the response. There is a need. A combination of this physical model and the resulting constitutive equation is also called a constitutive equation model. This invention provides a constitutive model that takes into account the accommodation behavior of the transformation behavior of shape memory alloys. In the following, a constitutive model is simply called a model.

In order to describe the accommodation behavior in the transformation of shape memory alloys, polycrystalline shape memory alloys are expressed as aggregates of grains with different crystal orientations. When the microscopic elements of the material expressed by these aggregates are embedded in the macroscopic material, the crystal grains in each orientation in the microscopic element cannot be freely deformed due to displacement constraints from surrounding materials. In order to express this, we consider a model in which the strain of crystal grains in each orientation is equal to the external strain (strain applied to the microscopic element of the material: strain applied from outside the aggregate of crystal grains). In this model, the microscopic elements of the material are represented by parallel coupling of grains with different orientations as schematically shown in Fig. 1. In this model, the strain of each grain is equal to the external strain, so it is also called an equistrained model.

If a transformation occurs in any of the grains in this model, the transformation strain occurs in that grain, resulting in a decrease in elastic strain and a decrease in stress. Therefore, the next transformation will occur in other grains, and a transformation in the direction that cancels the transformation strain that has already occurred will occur. In this way, the accommodation behavior of the transformation strain is described.

When considering the strain of a single crystal grain, if the transformation strain is generated in the entire crystal grain at one time, the transformation inherent strain is as large as 10%. Becomes unstable.
As shown in Fig. 2, a single crystal grain is further subdivided into N sub-elements having the same crystal orientation as the crystal grains, and different transformation limit stresses are applied to each sub-element, thereby transforming the transformation strain. Can occur for each subelement. At this time, the transformation strain of the grain is the average of the transformation strains of the N subelements, and 1 / N of the transformation inherent strain caused by the transformation of one subelement is the transformation of the grain caused by one transformation. Strain. By giving a large value to N, the transformation strain that occurs in each crystal grain can be reduced, and instability of the calculation can be prevented.

The transformation strain of the grains is the average of the transformation strains of these subelements. The elastic strain of a crystal grain is obtained by subtracting this average transformation strain from the value of the external strain, and from this, the stress of the crystal grain can be calculated.

The stress of the subelement is assumed to be equal to the stress of the crystal grain thus obtained. In other words, the subelements are represented by series connection within the crystal grains. This is shown in Fig.2.

Since one crystal grain has 24 transformation directions, the decomposition shear stress acting on each transformation plane is calculated from the stress obtained as described above, and the maximum value is the limit value. If it exceeds, the transformation will occur.

It is also possible to consider the effect of normal stress acting on the transformation surface. The transformation driving stress τ _DR is specifically expressed by τ _DR = τ + ασ.
However, τ is the decomposition shear stress, σ is the normal stress acting on the transformation surface, α is the material constant transformation driving stress, and the occurrence of transformation strain is evaluated.

For the limit value of transformation, the limit value at which transformation will occur and the element that has already undergone transformation will be restored to its original value when it is less than that, that is, the limit value for reverse transformation may be set. it can. Moreover, the limit value of transformation rearrangement in which the transformation direction changes when the limit value is exceeded can be set.

By setting the above limit values as a function of temperature, it is possible to describe not only the mechanical load but also the transformation behavior of shape memory alloys with respect to temperature changes.

The stress of the microscopic material element is the average of the stress of each crystal grain.

The above series of calculations proceeds with careful attention to the transformation of physical quantities in material coordinates, crystal grain coordinates (sub-element coordinates), and transformation plane coordinates.
Figure 3 shows the calculation procedure. That is,
Step 1: Give a small increment dε of strain ε. At this time, the strain is ε + dε.
Step 2: Obtain the strain of the subelements in each crystal grain. Due to the assumption of constant strain, this value is equal to ε + dε. However, since this strain is defined by the macro coordinates of the material, it is converted to the strain in the micro coordinates of the subelement by coordinate transformation. The elastic strain is obtained by subtracting the transformation strain of the subelement.
Step 3: Multiply the elastic strain by the elastic modulus to obtain the stress of the subelement (micro stress). Since there are 24 transformation systems for subelements, the decomposition shear stress considering the orientation of the transformation plane is obtained for each of them.
Step 4: Find the subelement that generates the maximum decomposition shear stress. If the maximum shear stress satisfies the transformation condition, give the transformation strain to this subelement and update the transformation strain value. The elastic strain is updated using the updated transformation strain value. The microstress value is updated using this.
Step 5: Convert stress in micro coordinates to stress in macro coordinates by coordinate transformation. This stress is averaged over the structure shown in Fig. 2, and this is the macro stress. This process gives the macro stress when the macro strain is applied at each incremental stage. By giving initial values and repeatedly calculating temperature and load increments according to the temperature and load conditions, the history of stress and strain at the given temperature and load conditions can be calculated.

As a specific example of the above calculation, Fig. 4 shows a calculation example of the superelastic behavior of a shape memory alloy.
Fig. 4 is an example of calculation of the superelastic behavior of a shape memory alloy. When uniaxial tensile stress is applied to a shape memory alloy in the austenite state (temperature range above the Af point), martensitic transformation occurs as the stress increases, and the gradient of the stress-strain curve becomes gentle. As the deformation further progresses and the martensitic transformation is saturated, the stress-strain curve rises due to the elastic deformation of the martensite. Next, in the unloading process, the austenite reverse transformation occurs when the stress falls below a certain stress, and after the saturation of the austenite reverse transformation, it returns to the origin of stress and strain. This series of stress / strain behavior is shown.

In the present invention, in order to accurately predict the stress / strain behavior accompanying the phase transformation of the shape memory alloy, the present invention is realized by a measurement method that incorporates the occurrence of the phase transformation behavior under the accommodation mechanism.
That is, when the stress-strain relationship of the superelastic behavior of the shape memory alloy is calculated by the measurement method of the present invention, the stress-induced martensite transformation start stress (strain), the transformation end stress (strain), and the unloading process This makes it possible to clarify the reverse transformation start stress (strain) and the reverse transformation end stress (strain) from the martensite phase to the austenite phase. ). Moreover, it is impossible to accurately determine the start and end of transformation and reverse transformation experimentally, which is of great academic and industrial significance.

Claims (1)

A polycrystalline shape memory alloy is shown by parallel connection of grains with different crystal orientations, and each grain is further divided into sub-elements. The average transformation strain of the sub-elements is taken as the transformation strain of the crystal grains. From this, the elastic strain and stress of the grains are obtained, and the decomposition shear stress at each transformation surface of each grain is obtained. When the maximum shear stress satisfies the transformation condition, the transformation strain is given to the subelement and the value of the transformation strain is calculated. , Update the elastic strain using the updated transformation strain value, update the microstress value using this elastic strain, convert the microstress to the macrostress in the macro coordinate, Considering the accommodation behavior of polycrystalline shape memory alloy, which is characterized by averaging this stress over the material structure including the subelements and making this a macro stress Phase transformation behavior measurement methods.