JPH0643924B2 - Method for measuring thermal stress in composite materials - Google Patents

Description

Description: TECHNICAL FIELD The present invention relates to a method for measuring thermal stress of a composite material, and in particular,
The thermal stress and residual stress of the plastic composite material are newly incorporated into the measuring method of the time and temperature dependence of the elastic modulus of the material so that the above stress at the joint interface can be predicted and measured with high accuracy. The present invention relates to a method for measuring thermal stress of a composite material.

[Conventional technology]

Conventionally, when measuring the thermal stress of a composite material under thermal stress, E and α obtained at a certain constant temperature and a certain speed are taken into consideration without considering the time and temperature dependence of the elastic modulus E and the linear expansion coefficient α of the material. It was used for measurement and analysis. Therefore, there is a fundamental problem that the absolute value of the stress obtained by the conventional method is poor in accuracy, and the residual stress cannot be measured when an uneven temperature distribution occurs in an object made of a single substance.

Originally, the physical properties of plastic materials change greatly continuously with time and temperature, and conventional methods that do not take this into consideration are inaccurate.

[Problems to be solved by the invention]

The mechanical behavior of plastic materials is highly time- and temperature-dependent. That is, for example, the elastic modulus, which is a measure of easiness of deformation, is generally large at low temperatures and small at high temperatures. Also, the coefficient of linear expansion is small at low temperatures and large at high temperatures.

However, the prior art does not take into consideration the time and temperature dependences of the elastic modulus E and the linear expansion coefficient α of the material, and it is measured using the constant values of E and α obtained at a certain constant temperature and a certain speed. -It was analyzed and there was a big problem in terms of accuracy of thermal stress. In particular, when discussing the strength of the joint interface in a composite material, the conventional method has a problem in accuracy, so accurate evaluation cannot be performed, and cracks and peeling may occur after leaving the manufacturer and entering the market. It was happening.

The object of the present invention is to be able to accurately measure the thermal stress and residual stress of a composite material, and to appropriately design and select the material, structural process conditions, etc. of the composite material based on the stress obtained by this measuring method. An object of the present invention is to provide a method for measuring the thermal stress of a composite material that can provide a guideline.

[Means for solving problems]

The above object is achieved by taking into consideration the time dependence and temperature dependence of the elastic modulus E and the linear expansion coefficient α, which are measures of the easiness of deformation of the material, in the measurement and analysis of the thermal stress.

[Action]

Generally, the elastic modulus E of a material is large at low temperature and small at high temperature. Therefore, when the changes of the elastic modulus E with respect to the temperature T and the time t are arranged, E is given by a single smooth curve with respect to t or T. Therefore, this E is approximated to a certain series (Proni series) and used for calculation.
On the other hand, the temperature change of the linear expansion coefficient α is measured in advance, and the strain is obtained using this. Then, the correspondence rule between temperature and time is obtained. By the above method, the thermal stress and residual stress of the first substance and the second substance constituting the composite material are measured.

〔Example〕

In recent years, so-called composite parts have been remarkably developed in which plastic materials are used in combination with different materials such as metals and ceramics, and their applications are also diverse. In the case of such a composite part, the reliability of stress and strength at the joint interface part is inevitably important because it is a combination of materials having different thermal and mechanical properties. Specifically, it is a matter of how to select the material and how to determine the size and structure. Therefore, although the problem of the bonding interface has been widely studied in the world, the current situation is that a sufficient technique for responding to this has not been established yet.

In the stress analysis of this type of composite part under thermal stress, the current technology is to obtain the physical properties such as the elastic modulus and linear expansion coefficient of the material under the condition of a certain temperature and a certain speed. Was being analyzed using. However, in this conventional method, if the physical property value used changes, the stress naturally changes, so that the true stress cannot be grasped, which is a serious problem. Originally, although the elastic modulus of a plastic material differs between low temperature and high temperature by about 1 to 2 orders of magnitude, a conventional method that does not take this into consideration is a problem.

Therefore, in the measuring method of the present invention, the elastic modulus and linear expansion coefficient of the material can be varied over a wide range from low temperature / short time region glass-like region to high temperature / long time region rubber-like region. Under the temperature condition, the above-mentioned physical property values are obtained in advance, and the stress is measured using this.

Next, the procedure of the stress measurement method will be outlined for two types of substances. First, the time change of the temperature T is obtained by the thermal analysis of the first substance and the second substance that form the composite part. Next, using the linear expansion coefficient α of the material, the strain ε _f that freely expands and contracts is obtained. Then, a coefficient representing the correspondence between time and temperature is experimentally obtained, and the conversion time t ′ for converting the temperature into time is calculated based on the coefficient. Next, necessary characteristics are calculated from the equation of the balance of stress and moment when the two materials are joined, and finally the strain ε ^* and the thermal stress σ are obtained. When obtaining this thermal stress, the characteristics of the above-mentioned change in elastic modulus with time are approximated to a series and used.

Hereinafter, as one embodiment of the present invention, a measurement method for obtaining a thermal stress distribution (or residual stress distribution) that occurs when both end surfaces of a two-layer model (a laminated strip of material A and material B) is rapidly cooled will be described in detail. Explained.

(Shape of Target Laminated Strip) Consider a laminated strip having a rectangular cross section composed of the material A and the material B as shown in FIG. Then, a Cartesian coordinate system in which the depth direction is x, the thickness direction is y, and the longitudinal direction is z is provided, the joint interface portion between the material A and the material B is set to x = 0, and the end surface of the material A is set to x =
-A, the end surface of the material B is x = b. Here, assuming that the length of the strip is the depth of the material A is d _A , the depth of the material B is d _B , the total depth is d (= d _A + d _B ), and the thickness is h, these The relationship is >> d >> h.

(Physical Property Values of Materials Used for Calculation) The material A constituting the laminated strip used in this example is an epoxy resin, and the material B is aluminum (JIS5052).
The epoxy resin was prepared by mixing Epicoat 807 as a main agent and Epicure T as a curing agent in a weight ratio of 100: 22, and after injecting into a mold of 150 mm ^□ , heat curing at 60 ° C. for 2 hours, and processing into a band plate having a predetermined size. Then, this was subjected to secondary curing at 200 ° C. for 1 hr and bonded to an aluminum strip to produce a laminated strip shown in FIG. Table 1 shows main physical property values of the material A and the material B.

(Method of measuring thermal stress) The entire strip shown in FIG. 1 is kept at the quenching temperature T _Q for a time t =
At 0, the upper surface (x = b) and the lower surface (x =
Consider the case where -a) becomes the cooling temperature T _C. At this time, both side surfaces (y = ± h / 2) of the strip are heat-insulated, and the thermal conductivities k _A and k _B of the materials A and B are constant and do not change with temperature. Under this condition, the temperature distributions T _A (x, t) and T _B (x, t) inside the strips of the materials A and B are derived from the one-dimensional unsteady heat conduction equation as follows.

From initial conditions, at t = 0, T _A (x, 0) = T _Q , T _B (x, 0) = T _Q
(3) From boundary conditions Therefore, when the equations (1) and (2) are solved under the conditions of the equations (3) to (7), the desired temperature distributions T _A (x, t) and T are obtained.
_B (x, t) is given by the following equation.

here, lambda: thermal conductivity, [rho: density, C: specific heat Safuikkusu A, respectively B material A, T _A obtained by the above method of representing the B (x, t), T B (x, t) the material caused by A , B thermal stress σ _tA (x, t), σ
_tB (x, t) and constraint strain σ _tA ^* (x,
t), σ _tB ^* (x, t) occurs only in the longitudinal direction (z direction) and is a function of location x and time t. And σ _tA (x, t), σ _tB (x, t) and σ that change _from moment to moment
_tA ^* (x, t) and _σtB ^* (x, t) can be calculated by the following equations if the time-temperature conversion rule is satisfied for the viscoelastic body.

Here, E _r (t ′, T _o ): relaxation modulus at the reference temperature T _o , α (T): linear expansion coefficient at the temperature T, (t): strain due to expansion / contraction in the longitudinal direction of the entire strip, t ′ , Τ ′: converted time, K (t): curvature of the strip plate interface, and suffixes A and B represent materials A and B, respectively.

On the other hand, t'is calculated from the time / temperature transfer factor a _To (T) by the following equation.

Here, strain (t) and curvature K of materials A and B
Since (t) becomes equal at the joint interface, _A (t) =
_B (t) = (t) and K _A (t) = K _B (t) = K
(T). Then, (t) and K (t) are obtained from the following stress balance and moment balance integral equations.

As described above, the equations (15) and (16) are satisfied (t), K
Equation (12), Equation (13), Equation (10), and Equation (11) are obtained by obtaining (t).
The thermal stresses σ _tA (x, t), σ _tB (x, t) and strains due to restraint ε _tA ^* (x, t) and ε _tB ^* (x, t) are calculated. Further, σ _t (x, t), ε _t ^* (x, t) and K (t) are still in a state where sufficient time has elapsed after the rapid cooling and the entire strip has a uniform cooling temperature T _C. When remaining, these become residual stress σ _A (x), σ _B (x), residual strain ε _A ^* (x), ε _B ^* (x) and residual curvature K.
Since the residual strain in this state is not distributed in the x direction, the constant values ε _A ^* and ε _B ^* can be calculated from equations (12) and (13) ^.
It is easy to see that

(Example of measurement result) The theoretical calculation was performed on a laminated strip of an epoxy resin (material A) that exhibits viscoelastic behavior and satisfies the time-temperature conversion rule, and aluminum (material B) that exhibits elastic behavior. That is, in the strip shown in FIG. 1, a = 2 mm, b = 20
Based on the theory of heat conduction and linear viscoelasticity, the temperature distribution inside the strip and the residual stress when the upper and lower end faces are rapidly cooled under the temperature conditions of T _Q = 180 ° C and T _C = 10 ° _C I calculated.

(Result of Calculation of Temperature Distribution) The temperature distribution T (x, t) inside the strip was calculated by the equations (8) and (9) using the physical property values shown in Table 1. The calculation result is shown in FIG. From this figure, it can be seen that the temperature of the aluminum portion drops sharply, whereas that of the resin portion slows down and is symmetrical with respect to the central portion. Next, the viscoelastic stress was calculated using these results.

(Example of Calculation Results of Residual Stress) (i) Calculation of Residual Stress The physical property values shown in Table 1 were used for the epoxy resin and aluminum described above. Further, the relaxation modulus E _r (t ′, T ₀ ) shown in FIG. 3 is obtained and the Star curve is approximated by a Proni series, and the time-temperature transfer factor a _To (T) shown in FIG. These two values were used by approximation with two different Arrhenius equations.

(Ii) Example of Calculation Results The results calculated by the above viscoelasticity theory are shown in FIG. From this figure, the residual stress is compressed near the cooling surface of the resin (material B) and becomes tensile at the joint interface portion, while it is tensile near the cooling surface of aluminum (material A) and becomes large compression at the joint interface portion. I understand.

On the other hand, in the elastic analysis, as the longitudinal elastic modulus E corresponding to the relaxation modulus E _r (t ′, T ₀ ), the value E _G at low temperature and glass, the value at intermediate temperature and viscoelastic region Calculations were made by selecting three levels for obtaining E _M and the value E _R at high temperature and rubber. At this time, the linear expansion coefficient α uses the average value α _M on the low temperature side and the average value on the high temperature side, and the results of these three levels of elastic analysis are shown in FIG. Comparing Fig. 5 and Fig. 6, the calculated value by ordinary elasticity analysis (Fig. 6) is different from the calculated value by viscoelastic analysis (Fig. 5) and the distribution state of residual stress is significantly different, and It can be seen that the elastic modulus E largely depends on the value. Therefore, the residual stress at the bonded interface portion of the laminated strip greatly affects practical problems such as the strength and peeling of the interface, and further the temporal deformation, so that it is important to measure this accurately. For this purpose, an analysis method considering the viscoelastic behavior proposed in the present invention will be further required in the future. Based on the thermal stress and residual stress obtained by the proposed measurement method, the material selection and shape determination of the composite material,
It is possible to optimize the process conditions, and it is possible to realize a designing and manufacturing method linked to improving the reliability of the interface.

〔The invention's effect〕

According to the present invention, the thermal stress and the residual stress of the composite material can be measured with high accuracy. Therefore, (1) the stress at the joint interface portion is accurately grasped, and the strength and reliability are excellent. Material design is possible. (2) Appropriate material selection based on stress and shape / structure design such as thickness can be done. (3) Proper selection of process conditions such as temperature condition to reduce generated stress. (4) The time variation of stress inside the material can be grasped moment by moment, so the cause of the accident such as clutch and peeling can be investigated. (5) The temperature of not only composite material but also single material The residual stress can be measured based on the non-uniformity, and so on.

[Brief description of drawings]

FIG. 1 is a shape diagram of a laminated strip used for explaining the embodiment, and FIG.
The figure shows the temperature distribution inside the strip as a result of calculation, Fig. 3 shows the relaxation modulus of the material, Fig. 4 shows the time-temperature transfer factor, and Fig. 5 shows the viscoelasticity of the residual stress distribution of the composite material. FIG. 6 is a diagram showing a solution, and FIG. 6 is a diagram showing an elastic solution of residual stress distribution. <Explanation of symbols> 1 ... Joined interface

 ─────────────────────────────────────────────────── ─── Continuation of the front page (72) Gen Murakami, 1450 Kamimizuhonmachi, Kodaira-shi, Tokyo Inside Musashi Factory, Hitachi, Ltd. (72) Yasushi Miyano, 3-14-8 Izumino-cho, Kanazawa-shi, Ishikawa Prefecture

Claims (1)

[Claims] 1. A plastic composite material composed of a combination of a material such as metal or ceramic and a plastic material, wherein the elastic modulus and linear expansion coefficient of each material constituting the composite material changes with temperature, and the elastic modulus changes with time. Is measured in advance, and a continuous change in the elastic modulus with respect to the conversion time obtained by converting the temperature into time is obtained from these measured values, and the thermal stress and the residual stress at the joint interface portion of the composite material are determined by the temporal change characteristics of the elastic modulus. A method for measuring the thermal stress of a composite material, characterized by using a series approximation.