JPS58162838A - Method for analyzing elastoplastic stress - Google Patents

Abstract

PURPOSE:To determine a stress state quantitatively with respect to general structures, by writing down the rule of hardening by movement, the rule of flow, etc. with respect to a plane stress state by the use of a bilinearly approximated stress-strain relation. CONSTITUTION:The stress-strain curve a of material is bilinearly approximated by an alternate long and short dash line c. The rule of hardening by movement using the initial yield conditions of Von Mises, the rule of flow of Prandtl Lewis and the relations between the quantity of hardening by movement and strain are written down with respect to a plane stress state as the equations for describing the plastic stress state. young's modules E and coefft. C of work hardening are determined from monoaxial tension tests of material, and the strain increments in the two directions of the noticed points are measured continuously with strain gages and are substd. in the equations. The stress increments, the equivalent plastic strain increments and the extents of movements of the origin of the yield curve are determined. The stress analysis which takes work hardening and Bauschinger effect into consideration is accomplished and the behavior of plastic stress and residual stress are determined quantitatively.

Description

DETAILED DESCRIPTION OF THE INVENTION The present invention relates to an elasto-plastic stress analysis method for quantitatively determining the stress state of general structures in which steam generator heat transfer tubes, laminar stress, and residual stress pose problems in terms of strength.

The stress-strain-a+ of an actual material enters the plastic range from the elastic range, as shown in the figure, and work hardening and parasin are effective in the plastic range. Conventionally, when determining the stress state of this material quantitatively, it is easy to handle logically. The elastoplastic strain is converted into stress by adjusting the needle side with r-ji.

That is, the analysis procedure of the conventional method using the elastic-perfect plasticity approximation as the material property is as follows.

stt d σ11 + S snow 3 d σtomi* =
O(1)d 1fit , dσ2. t-measure and calculate the unknown quantity doo using equations (1), (2), and (3).
r d#zz+ d'1yt-calculate.

Here, 11 + d81 is the stress increment, di is the stress plastic strain increment, and the amount of movement of the origin of the yield surface, that is, the effect of material work hardening and parasin, is not taken into account.For this reason, conventional approximation In this case, the actual stress state cannot be determined with high accuracy.

The present invention has been made in view of the above circumstances, and its purpose is to use a stress-strain relationship approximated by three straight lines in consideration of work hardening and the Paushinger effect, as shown at a point @ line C in the drawing. In particular, we aim to obtain an elastic-plastic stress analysis method that can accurately determine the stress state s' and can be effectively used as basic data for stress corrosion cracking countermeasures for structures and products that undergo plastic deformation. be.

In other words, the present invention uses a trilinear approximation of the stress-strain relationship to obtain a formula indicating the plastic stress state m from the amount of kinematic hardening, the flow law, and the relationship between the amount of kinematic hardening and strain, and then uses the open formula to measure strain by plasticity experiments. This is an elasto-plastic stress analysis method characterized by 1-1, which calculates the plastic stress, plastic strain, and amount of kinematic hardening by inputting the values.

The present invention will be explained below with reference to Figure mt. In the present invention, as a formula to describe the plastic stress state 11+, the initial a yield condition of Van Misss is used, and the friend movement hardening law, Prandtl-Reuss (Prandtl-R@u
(2) The flow law and the relational expression between movement hardening amount and strain are used as the auxiliary agent.

Movement hardening amount 2 (Sij-α,j) (8,,-α,),,F 0
- (4) Flow law auxiliary agent (relationship between movement hardening amount and strain) dα, = cdgPlj - (6) j aij ' Stress tenor Jj: Deviation stress tensor α: Movement amount tensor i 1i'' - Strain tensor (measured value) dl P: Plastic strain increment j aij: Kronet force - delta dσxz = d e■ + d 1g 133σ
Y: Yield stress E: Young's modulus ν: Boann ratio iP: Equivalent plastic strain C: Work hardening coefficient (material constant) %j: Tensor subscript 1=1~3j=1~3 Next, the above relationship is expressed as In the following, the subscript 11.11.31 indicates the principal stress (principal strain) direction. The plane stress state we are currently considering is σss ”o.

Transfer hardening amount (incremental form of equation (4)) Flow law (formula (5)) Auxiliary agent (formula (6)) Now, Young's modulus E is determined by the uniaxial tensile test of the material.

Determine the work hardening coefficient cl. In addition, in the plasticity test, the strain increments d#11. d
(** Measure continuously and enter them into equations (7) to (2) to solve this simultaneous six-element linear equation.

Then, stress increment dσ11+dσ■1 equivalent plastic strain increment djp+movement amount of the origin of yield surface dα11. dα■.

dα33 Move to Tokyo.

Here dαB, dα! 3. dαms is a physical quantity expressing the work hardening of the material and the Paushinger effect.

As described above, according to the present invention, by using the stress-strain relationship approximated by trilinear lines, it is possible to perform stress analysis that takes work hardening and the Paushinger effect into consideration, and to accurately estimate plastic stress behavior and residual stress. It can produce remarkable effects.

[Brief explanation of the drawing]

The drawings are diagrams showing the stress-strain relationship for an actual material, a conventional elastic-perfect plastic approximation straight line, and a bilinear approximation straight line according to the present invention. Applicant Sub-Agent Patent Attorney Takehiko Suzue-2 (

Claims (1)

[Claims] Using the stress-strain relationship approximated by two lines, the amount of movement hardening,
Determine the formula that indicates the plastic stress state from the flow law and the relationship between the amount of kinematic hardening and strain, and calculate the plastic stress, plastic strain, and amount of kinematic hardening by inputting all the measured strain values from the same large KWi experiment t-% An elastoplastic stress analysis method based on images.