JP4580747B2 - Measuring method for plastic zone dimensions - Google Patents

Description

  The present invention relates to a plastic region size measuring method for estimating a size of a plastic region generated at a stress concentration portion of a member.

  As seen in car body frames and the like, thin steel plates are actively used in recent structures for the purpose of weight reduction. By the way, the damage generated in these structures is often caused by the result of stress concentration in the notch or the like processed into a thin steel plate. Therefore, it is important to evaluate the strength of the stress concentration portion.

  There is a possibility that plastic deformation is locally generated in the stress concentration portion, and there is a plastic region dimension as a parameter for estimating the strength of the local plastic portion. However, it is often virtually impossible to detect the plastic zone size of a structure already assembled using, for example, a strain gauge.

Therefore, in recent years, focusing on the fact that strain energy generated when a member is deformed is mostly converted into thermal energy in the plastic deformation region, a plastic region dimension measurement method using an infrared camera has been proposed (for example, Non-patent document 1).
National Welding Society Annual Conference Summary Vol. 51 ('92 -10) pp. 276-277

  However, since the heat generated in the member due to plastic deformation is transferred to the outside of the plastic region due to the heat conduction characteristics of the material, it is not only necessary to measure the temperature of the member to accurately investigate the behavior of the temperature rise. It is essential to consider.

  There have been several reports on the investigation of heat generation behavior due to plastic deformation so far, but only the temperature is estimated by calculation such as FEM (finite element method), and systematic including heat generation and heat transfer characteristics has been reported. None of the studies investigated the relationship between the plastic zone size and temperature rise. Moreover, complicated analysis is required to estimate the plastic region from the temperature measured by the infrared camera.

  Furthermore, in order to investigate the effects of plastic deformation, it is common practice to apply a tensile load to a member from one direction, but most of the assembled members are tested (or operated) under repeated load conditions. ) Should be avoided as much as possible by adding other new loads.

  The present invention has been made in consideration of the problems in the conventional method for measuring a plastic region dimension as described above, and a plastic region dimension capable of measuring a plastic region dimension generated in a stress concentration portion of a member by a simple method. A measurement method is provided.

The present invention is a plastic area size measurement method for measuring a plastic area dimension caused by plastic deformation of a measurement object to which a repeated load is applied, and detects a temperature variation of the measurement object to which a repeated load is applied by an infrared sensor, An average temperature θ _m of temperature fluctuations in which heat generation and endotherm are repeated is obtained, and the maximum value of the difference (θ _m −θ ₀ ) between the average temperature θ _m and the initial temperature θ ₀ of the measurement object is determined as the maximum temperature increase t _max. When the strength / heat transfer parameter specific to the measurement object affecting the temperature fluctuation is a known number p,
The plastic zone size s is expressed by the following formula: Plastic zone size s ^1.7 = α ₁ · C · t _max / p
However, C is a constant that defines the center of variation in the estimated plastic zone size, and α ₁ is a plastic zone size measuring method that is determined by a correction factor that takes into account the allowable error in the plastic zone size.

  In the present invention, the plastic zone dimension means, for example, the maximum length in the crack progressing direction in a plastic zone generated at the tip of a crack-like defect.

In the present invention, by giving (yield stress ² / longitudinal elastic modulus) · [(density / specific heat / load frequency) / thermal conductivity] as the strength / heat transfer parameter p, the size of the plastic zone can be measured. it can.

The present invention is a plastic area size measurement method for measuring a plastic area dimension caused by plastic deformation of a measurement object to which a repeated load is applied. An average temperature θ _m of temperature fluctuations in which heat generation and endotherm are repeated is obtained, and the maximum value of the difference (θ _m −θ ₀ ) between the average temperature θ _m and the initial temperature θ ₀ of the measurement object is determined as the maximum temperature increase t _max. The object to be measured is either iron-based metal, aluminum-based metal, or titanium-based metal,
The plastic zone size s is expressed by the following formula: Plastic zone size s ^1.7 = α ₂ · F · t _max · Thermal conductivity / (Yield stress ² · Load frequency)
However, F is a constant corresponding to each metal, and α ₂ is a plastic area dimension measurement method obtained by a correction coefficient considering an allowable error of the plastic area dimension.

  According to the present invention, it is possible to estimate the plastic zone size of the plastic deformation portion in the measurement object by a simple method.

  Hereinafter, the present invention will be described in detail based on the embodiments shown in the drawings.

  FIG. 1 shows a member having a crack-like defect as a model in which stress is concentrated.

  In the figure, reference numeral 1 is a thin plate member (measurement object), and 2 is a crack-like defect existing in the member 1.

  A temperature investigation target part (measurement part) 3 is set for the tip of the crack-like defect 2 when a repeated load (tensile loads opposite to each other in the directions of arrows A and B) is applied to the member 1, and an infrared camera is used. The temperature fluctuations were measured using this method. The crack-like defect 2 is set to have the highest risk of destruction when a load is applied in the directions of arrows A and B.

  FIG. 2 schematically shows the measurement results. FIG. 2A shows a temperature change when the member 1 is not plastically deformed as a comparative example, and FIG. 2B shows the member 1. Shows the temperature fluctuation when plastic deformation occurs.

In both figures, the member 1 undergoes temperature fluctuations due to heat generation and absorption even if it is not plastically deformed, but if it is not plastically deformed, the same average temperature as in the initial state as shown in FIG. The temperature varies with θ ₀ as a boundary.

On the other hand, when plastic deformation occurs, only heat generation occurs when a repeated load is applied, so the average temperature gradually increases from the initial temperature θ ₀ and saturates at a certain temperature θ _m .

In the present invention, the plastic zone dimension s is measured using the temperature rise t _max at the time when it is sufficiently saturated (maximum value), and the influence of various factors described below is taken into consideration.
(1) Effects of various factors When plastic deformation occurs at the tip of the crack-like defect 2, the average temperature rises as described above, but the behavior of the temperature rise is considered to include the following effects.
a) the influence of the geometric plastic zone size, b) the influence of the material strength, and c) the influence of the heat transfer properties.

  Next, consider each of the above effects.

a) Influence of geometric plastic zone size When the exothermic characteristics and heat transfer characteristics of the material are exactly the same, the larger the plastic zone size, the greater the amount of heat generated at the crack tip and the greater the temperature rise. Conceivable. In order to investigate this influence, first, the strength and heat transfer characteristics are made the same conditions, and the influence when only the plastic zone size is changed is examined.

  The amount of heat generated by plastic deformation is considered to be proportional to the area of the plastic zone. When the shape of the plastic zone changes to a similar shape as the load condition changes, the area of the plastic zone is proportional to the square of the plastic zone size. However, since the shape of the plastic zone is complicated and does not necessarily change to a similar shape, it is assumed for the sake of convenience that the area of the plastic zone is proportional to the A-th power of the plastic zone size.

b) Effect of material strength When plastic deformation occurs, the amount of heat generated is considered to vary depending on the strength of the material. In order to investigate the influence, next, the heat transfer characteristic and the plastic region size are made the same, and the influence on the temperature change when only the material is changed is examined.

In general, the amount of heat generated by plastic deformation is proportional to the plastic work, and the plastic work at the tip of a crack-like defect is considered to correspond to the J integral, which is a parameter at the crack tip. The J-integral is proportional to (stress intensity factor) ² / (longitudinal elastic modulus) unless the plastic region is excessive. That is, the calorific value∝stress intensity factor ² / longitudinal elastic modulus.

On the other hand, the plastic zone is proportional to (stress intensity factor) ² / (yield stress) ² . That is, the plastic region ∝ stress intensity factor ² / yield stress ² is obtained.

From the above relationship, the relationship between the calorific value and the plastic zone is expressed as follows.
Calorific value ∝ (yield stress ² / longitudinal elastic modulus) x plastic area size s (1)
Here, assuming that the plastic zone dimension s is constant, the temperature rise is simplified to be proportional to (yield stress ² / longitudinal elastic modulus).

c) Influence of heat transfer characteristics Even if the amount of heat generated by plastic deformation is the same, if the heat transfer characteristics of the material are different, the behavior of the generated temperature will also be different. In order to investigate this influence, next, the influence when changing the heat transfer characteristic of the material with the same plastic zone size s and the strength of the material is examined.

  According to literature already published, when an object to which a load is repeatedly applied generates heat locally, the amount of temperature rise depends on the Fourier number. The Fourier number is a dimensionless number proportional to (thermal conductivity) / (density / specific heat / load frequency). The smaller the Fourier number, the larger the temperature rise, and vice versa. Becomes smaller.

  Thus, the temperature rise due to local heat generation is considered to be inversely proportional to the Fourier number, and can also be considered to be proportional to (density / specific heat / load frequency) / (thermal conductivity).

(2) Verification of various effects by analysis An analytical study was conducted to examine the effects of a) to c) described above. In the analysis, the crack tip was plastically deformed by forcibly applying repeated displacement to the analytical model shown in FIG. 1, and the plastic zone size s and the temperature increase were examined.

  In addition, since 90% of the plastic work is converted into heat as heat generation due to plastic deformation, in this analysis, the conversion rate from the plastic work to the heat generation amount was set to 90%.

  In the analysis in the present embodiment, the load ratio (minimum load / maximum load) was set to 0, and the tension piece swinging condition was set. Actual members and structures are often under both tensile and compression conditions, but if there are crack-like defects 2, stress concentration does not occur during compression and there is no substantial defect. Because it can be considered, there is no problem in considering only under the tension swinging condition.

  In the following description, the maximum temperature rise at the tip of a crack-like defect is used as the temperature rise.

(2-a) Influence of plastic zone dimensions Several conditions of plastic zone dimensions were analyzed with the same conditions except for the plastic zone dimensions. The analysis conditions and temperature conditions are shown in Table 1.

Moreover, the change of the maximum temperature rise amount is shown in FIG. In the figure, the horizontal axis represents the plastic zone dimension s (mm), and the vertical axis represents the maximum temperature rise t _max (K).

If the maximum temperature rise corresponding to the plastic zone size in Table 1 is plotted on a graph and each plot is connected by a curve, it can be seen that the maximum temperature rise t _max and the plastic zone size s are proportional, and the maximum temperature rise is It is determined by 0.03 × plastic zone size s ^1.7 . Therefore, for the sake of convenience, A that is assumed to be the A-th power of the plastic zone dimension can be determined to be 1.7.

(2-b) Effect of material strength The conditions other than the yield stress and the longitudinal elastic modulus were the same, the yield stress and the longitudinal elastic modulus were set to several conditions, and the relationship with the temperature rise was obtained. The conditions and results are shown in Table 2.

Further, FIG. 4 shows a change in the maximum temperature increase t _max under these conditions. In the figure, the horizontal axis represents the yield stress ² / longitudinal elastic modulus (MPa), and the vertical axis represents the maximum temperature rise t _max (K). As shown in the figure, the maximum temperature rise t _max is proportional to the yield stress ² / longitudinal elastic modulus.

(2-c) Effect of heat transfer characteristics The heat transfer characteristics were set to several conditions with the same plastic zone size and heat generation characteristics of the material, and the relationship with the temperature rise was obtained. The conditions and results are shown in Table 3.

In addition, FIG. 5 shows the change in the maximum temperature increase t _max under these conditions. In the figure, the horizontal axis indicates density, specific heat, frequency / thermal conductivity, and the vertical axis indicates the maximum temperature rise t _max (K). As shown in the figure, the maximum temperature rise t _max is proportional to the density, specific heat, frequency / thermal conductivity.

(2-d) Formulation of Maximum Temperature Rise From the results of examining the above influencing factors, the maximum temperature rise t _max is expressed as follows by multiplying 3 influencing factors.
Maximum temperature rise t _max = B · Plastic zone size s ^1.7 · (Yield stress ² / Longitudinal elastic modulus) · (Density, specific heat, frequency / thermal conductivity) …… (2)
However, the constant B is determined so that the value of each factor multiplied and the maximum temperature rise amount correspond to 1: 1.

FIG. 6 shows the relationship between the maximum temperature rise t _max and the plastic zone size s ^1.7 · (yield stress ² / longitudinal elastic modulus) · (density / specific heat / frequency / thermal conductivity) for all analysis results. In this figure, the horizontal axis shows the plastic zone size s ^1.7 · (yield stress ² / longitudinal elastic modulus) · (density, specific heat, frequency / thermal conductivity), and the vertical axis shows the maximum temperature rise t _max (K). ing. As shown in the figure, it can be seen that the maximum temperature increase t _max is proportional to the horizontal axis value.

(2-e) Plastic zone size estimation formula The plastic zone size is obtained as follows from the above-mentioned formulation.
Plastic zone dimension s ^1.7 = C · Maximum temperature rise t _max / [(Yield stress ² / Longitudinal elastic modulus) · (Density, specific heat, frequency / thermal conductivity)] …… (3)
Note that the constant C at this time is 27, which defines the center of variation in the estimated plastic region size.

In addition, [(yield stress ² / longitudinal elastic modulus) · (density / specific heat / frequency / thermal conductivity)] on the right side of Equation (3) is the strength / heat transfer that affects the temperature variation of the plastic deformation part of member 1 It can be regarded as the parameter p.

Next, for all the analysis results, the relationship between the plastic zone size s ^1.7 and the maximum temperature rise t _max / [(yield stress ² / longitudinal elastic modulus) · (density, specific heat, frequency / thermal conductivity)] As shown in FIG. In the figure, the horizontal axis indicates the maximum temperature rise t _max / [(yield stress ² / longitudinal elastic modulus) · (density, specific heat, frequency / thermal conductivity)], and the vertical axis indicates the plastic zone size s ^1.7. Yes. As shown in the figure, it can be seen that the plastic zone size s ^1.7 is proportional to the horizontal axis value.

(2-f) Consideration of variation Although the analysis result is well expressed by the estimation equation (3), there is variation. Here, the amount of variation allowed in the strength evaluation was examined, and the analysis results were verified.

  For the purpose of elucidating the characteristics of crack propagation and evaluating the remaining life when the existence of crack defects is assumed in advance, a crack growth test is performed on a specimen having crack defects.

  In a typical crack growth test, the load amplitude and the average load are made constant, and the crack length a when the number of repetitions is N is measured.

  The crack growth rate da / dN means the crack length that propagates by one stress repetition, and is usually shown with respect to the stress intensity factor width ΔK.

The intermediate region excluding the lower limit and the upper limit where the crack does not propagate is a stable region showing the crack growth rate, and is usually represented by the following Paris-Erdogan equation.
da / dN = A (ΔK) ⁿ (4)
Here, A and n are material constants, and the value of n is often about 2 to 7 for metals.

  Therefore, in applying the estimated plastic zone to strength evaluation for crack growth, the plastic zone is converted into the stress intensity factor width ΔK, and the life is predicted from the crack growth rate.

  The graph showing the relationship between ΔK and crack growth rate is expressed in logarithmic scales on the horizontal and vertical axes, and the crack growth rate is considered to be an error up to 2 to 1/2 times (double or half). ing.

  When converted to ΔK (n = 7), the allowable error of the double / half crack growth rate is ± 10%.

Further, since the plastic zone size is proportional to the square of the K value, the tolerance of ± 10% ΔK becomes the tolerance of the plastic zone size of about ± 20%. A correction coefficient taking this tolerance into account is α ₁ , which is shown in FIG.

  From this figure, it can be confirmed that the variation in the analysis results is within the allowable error range. Further, when the plastic region is estimated, it may be estimated within the variation W shown in the figure, and it can be evaluated most safely by adopting the value of the upper limit (see the characteristic L in the figure).

Here, let D be a constant that takes into account the correction coefficient α ₁ and a constant C that defines the center of variation in the estimated plastic zone size.

The characteristic L is represented by the following formula.
Plastic zone size s ^1.7 = D ・ Maximum temperature rise t _max / [(yield stress ² / longitudinal elastic modulus) ・ (density, specific heat, frequency / thermal conductivity)] ...... (5)
The constant D at this time is 32.

(2-g) Proposal of estimation formula based on material The materials used for structures and parts include steel, aluminum alloy, titanium alloy, etc., but the modulus of elasticity, density, and specific heat are almost the same for each material. It becomes the same value. For example, if the material used is steel, the above characteristics hardly change even if the strength level changes. Therefore, an estimation formula for each material can be created by utilizing this characteristic.

  Table 4 below shows representative values of the longitudinal elastic modulus, density, and specific heat for each material.

Based on these numerical values, the estimation formula of each material is expressed as follows.
For steel (including ferrous metals, iron and iron-base alloys) Plastic zone size s ^1.7 = 57.4 × 10 ⁶ · D · Maximum temperature rise t _max · Thermal conductivity / (yield stress ² · frequency) = 1837 × 10 ⁶ · Maximum temperature rise t _max · Thermal conductivity / (Yield stress ² · Frequency) (6)
For aluminum alloys (including aluminum-based metals, aluminum and aluminum-based alloys) Plastic zone size s ^1.7 = 28.2 × 10 ⁶ · D · Maximum temperature rise t _max · Thermal conductivity / (yield stress ² · frequency) = 902 × 10 ⁶・ Maximum temperature rise t _max・ Thermal conductivity / (Yield stress ²・ Frequency) …… (7)
Titanium alloys (including titanium-based metals, titanium, and titanium-based alloys)
Plastic zone size s ^1.7 = 40.2 × 10 ⁶ · D · Maximum temperature rise t _max · Thermal conductivity / (Yield stress ² · Frequency) = 1286 × 10 ⁶ · Maximum temperature rise t _max · Thermal conductivity / (Yield (Stress ² / Frequency)… (8)

However, since the material constant F (for example, 1837 × 10 ⁶ ) varies around the representative value, the variation can be taken into account by multiplying the correction coefficient α ₂ by the right side of the estimation equation. For example, assuming that each constant has a variation of about ± 10%, it is necessary to correct the calculation result of the estimation formula in consideration of the variation of ± 30%.

(2-h) Verification of the estimation formula by actual measurement The test piece containing crack-like defects was repeatedly loaded, and the temperature rise at the tip of the defect was captured with an infrared camera, and the maximum temperature rise was measured.

  FIG. 9 shows a thin plate-like test piece 4 to which a repeated load is applied, 5 is a crack-like defect formed at the edge of the test piece 4, A and B indicate the tensile direction, and E is a defect. The part periphery is shown. FIG. 10 shows the temperature distribution around the defect E captured by the infrared camera.

  The measurement results are shown in Table 5 below. In addition, the plastic area dimension was calculated | required by performing FEM analysis with respect to the test piece 4 shown in FIG.

The relationship between the plastic zone dimension s ^1.7 and the maximum temperature rise t _max / [(yield stress ² / longitudinal elastic modulus) · (density, specific heat, frequency / thermal conductivity)] is indicated by x in FIG.

  As can be seen from the figure, the numerical value of x is within the range of the variation W, and the above-described formulation was verified.

  In the graph of FIG. 11, the slope of the line T represents the constant C, and the slope of the line U represents the constant D.

  (2-i) The plastic zone size according to the present embodiment is the largest, that is, the plastic zone size is estimated from the maximum temperature rise by using a line (indicated by a line U in FIG. 11) that is estimated on the safe side. be able to.

  However, since the resolution of the infrared camera is limited, it is difficult to read temperature fluctuations below a certain level.

  Therefore, the temperature distribution along the arrow H shown in FIG. 10 is shown in the graph shown in FIG.

  As shown in the graph of the figure, in addition to the temperature behavior due to plastic deformation, the temperature behavior due to noise is also seen. The temperature change due to the noise is considered to be 0.01 ° C., and even if there is a temperature rise of 0.01 ° C. or less due to plastic deformation, it is buried in the noise and becomes difficult to detect, and the measurement accuracy decreases.

  In other words, according to this estimation line, it is possible to estimate with a higher measurement accuracy for a temperature rise of 0.01 ° C. or more.

It is explanatory drawing of the crack-like defect model which concerns on embodiment of this invention. (a) is explanatory drawing which shows each temperature change when there is no plastic deformation, (b) is when there is plastic deformation. It is a graph which shows the relationship between a plastic zone dimension and the maximum temperature rise amount. It is a graph which shows the relationship between yield stress ² / longitudinal elastic modulus and the maximum temperature rise. It is a graph which shows the relationship between density, specific heat, frequency / thermal conductivity, and the maximum temperature rise amount. It is a graph which shows the relationship between the plastic zone size ^1.7 * (yield stress ² / longitudinal elastic modulus) * (density, specific heat, frequency / thermal conductivity), and the maximum temperature rise. It is a graph which shows the relationship between the maximum temperature rise / [(yield stress ² / longitudinal elastic modulus) * (density, specific heat, frequency / thermal conductivity)] and the plastic zone size. It is a graph which shows the tolerance of a plastic zone dimension. It is explanatory drawing which shows the test piece to which a repeated load is added. It is a temperature distribution figure of the test piece to which a load is repeatedly applied. It is a graph for demonstrating the formula which calculates | requires a plastic region dimension. It is a graph which shows the temperature behavior of the crack-like defect tip.

Explanation of symbols

1 Cracked Defect 2 Crack Defect 3 Temperature Survey Part 4 Test Specimen 5 Crack Defect E Defect Tip

Claims (3)

In a plastic area dimension measuring method for measuring a plastic area dimension caused by plastic deformation of a measurement object to which a repeated load is applied,
The infrared sensor detects temperature fluctuations of the measurement object to which repeated loads are applied,
Find the average temperature θ _m of temperature fluctuations where heat generation and heat absorption are repeated,
The maximum value of the difference (θ _m −θ ₀ ) between the average temperature θ _m and the initial temperature θ ₀ of the measurement object is obtained as the maximum temperature increase t _max , and is unique to the measurement object that affects the temperature fluctuation. When the strength and heat transfer parameters of a known number p,
The plastic zone size s is expressed by the following formula: Plastic zone size s ^1.7 = α ₁ · C · t _max / p
However, C is a constant that defines the center of variation in the estimated size of the plastic zone, and α ₁ is obtained by a correction factor that takes into account the allowable error of the plastic zone size. ^2. The plastic region dimension measuring method according to claim 1, wherein (yield stress ² / longitudinal elastic modulus) · [(density / specific heat / load frequency) / thermal conductivity] is given as the strength / heat transfer parameter p. In a plastic area dimension measuring method for measuring a plastic area dimension caused by plastic deformation of a measurement object to which a repeated load is applied,
The infrared sensor detects temperature fluctuations of the measurement object to which repeated loads are applied,
Find the average temperature θ _m of temperature fluctuations where heat generation and heat absorption are repeated,
The maximum value of the difference (θ _m −θ ₀ ) between the average temperature θ _m and the initial temperature θ ₀ of the measurement object is determined as the maximum temperature increase t _max ,
The measurement object is one of an iron metal, an aluminum metal, or a titanium metal,
The plastic zone size s is expressed by the following formula: Plastic zone size s ^1.7 = α ₂ · F · t _max · Thermal conductivity / (Yield stress ² · Load frequency)
Where F is a constant corresponding to each metal, and α ₂ is obtained by a correction factor that takes into account the allowable error of the plastic zone size.

Images