Effect of State-of-Stress and Yield Criterion on the Bauschinger Effect

1968 ◽  
Vol 90 (3) ◽  
pp. 403-408 ◽  
Author(s):  
S. T. Rolfe ◽  
R. P. Haak ◽  
J. H. Gross

During fabrication, the cold forming of structural components may reduce the yield strength of a component if it is loaded in a direction opposite to that of the cold forming. This reduction in yield strength, referred to as the Bauschinger effect, is influenced by the state-of-stress under which the cold forming is performed, by the criterion used to determine the yield strength, and by the use of post-forming stress relief. To establish the importance and magnitude of these effects, specimens from 2 1/2-in-thick plates of HY-80 steel, cold-formed by plane strain bending, were tested along with specimens that were cold-formed by plane-stress axial straining. For material tested in a direction opposite to that of cold forming, the Bauschinger effect was observed both in tension and compression, whereas for material tested at 90 deg to the direction of cold forming in plane strain, both the tensile and compressive yield strengths increased and no Bauschinger effect was observed. Because of the difference in restraint, the Bauschinger effect was greater for plane-stress axial deformation than for plane-strain bending deformation. The Bauschinger effect was greater when the yield strength was determined at small offsets and was essentially eliminated at an offset greater than 0.5 percent. In addition, the Bauschinger effect was greatest for small amounts of cold deformation and was progressively decreased by strain hardening at large amounts of cold deformation. The reduction in secant modulus and in yield strength (Bauschinger effect) in cold-formed material was essentially eliminated by stress-relief treatment at 1025 deg. F. The results indicate the importance of knowing the cold-forming state-of-stress, the criterion used in determining yield strength, and the effects of stress relief when assessing the effects of cold deformation on mechanical properties.

2020 ◽  
Vol 37 ◽  
pp. 100-107
Author(s):  
Sergei Alexandrov ◽  
Yeau-Ren Jeng

Abstract A general plastic material under plane strain and plane stress is classified by a yield criterion that depends on both the first and second invariants of the stress tensor. The yield criterion together with the stress equilibrium equations forms a statically determinate system. This system is investigated in the principal lines coordinate system (i.e. the coordinate curves of this coordinate system coincide with trajectories of the principal stress directions). It is shown that the scale factors of the principal lines coordinate system satisfy a simple equation. Using this equation, a method for constructing the principal stress trajectories is developed. Therefore, the boundary value problem of plasticity theory reduces to a purely geometric problem. It is believed that the method developed is useful for solving a wide class of boundary value problems in plasticity.


Author(s):  
Peihua Jing ◽  
Tariq Khraishi ◽  
Larissa Gorbatikh

In this work, closed-form analytical solutions for the plasticity zone shape at the lip of a semi-infinite crack are developed. The material is assumed isotropic with a linear elastic-perfectly plastic constitution. The solutions have been developed for the cases of plane stress and plane strain. The three crack modes, mode I, II and III have been considered. Finally, prediction of the plasticity zone extent has been performed for both the Von Mises and Tresca yield criterion. Significant differences have been found between the plane stress and plane strain conditions, as well as between the three crack modes’ solutions. Also, significant differences have been found when compared to classical plasticity zone calculations using the Irwin approach.


2021 ◽  
Vol 1016 ◽  
pp. 648-653
Author(s):  
Antti Kaijalainen ◽  
Juho Mourujärvi ◽  
Juha Tulonen ◽  
Petteri Steen ◽  
Jukka I. Kömi

The aim of this work is to study the effect cold forming rate (CFR) on the mechanical properties and microstructure of a conventional TMCP and a direct-quenched steel in 420 MPa strength level. The microstructure was characterized using FESEM-EBSD. Tensile properties and Charpy-V impact toughness were determined. As the CFR increased, the yield and tensile strength raised quite linearly with both steels. Yield strength values increased from 450 MPa (as-rolled material) to 700 MPa (25 % CFR). However, tensile strength increased less compared to yield strength. Uniform elongation decreased linearly till about 10 % CFR and total elongation till about 15 – 20 % CFR. The impact values decreased quite linearly in -40 °C and -60 °C test temperature when the cold forming rate increased. In longitudinal direction (L-T) the impact values were at high level at -40 °C and -60 °C with both steels with all CFR. In transverse direction (T-L) the impact results were lower. Impact energies were enhanced by direct quenching compared to conventional steel in every CFR stage. EBSD results showed no major difference between steels in the grain sizes in generally. However, cold forming decreased the grain size and increased low-angle grain boundaries in correlation with increasing CFR. Small size of the coarsest grains (d90%) usually indicate better toughness, however in this case the impact values were decreased even with smaller grain size as cold deformation occurs. On the other hand, the strength level increased with forming rate. Therefore, a brief discussion of the microstructural features controlling the impact toughness is given.


2019 ◽  
Vol 972 ◽  
pp. 105-110
Author(s):  
Sergei Alexandrov ◽  
Elena Lyamina ◽  
Yeau Ren Jeng

There are materials whose forward flow curve is practically independent of plastic strain (perfect plasticity) but the Bauschinger effect reduces the elastic range with flow reversal. A new model that is capable of describing such behavior of material under plane stress conditions has been recently proposed. An important class of structures in which the state of stress can often be accurately approximated by plane stress conditions is thin hollow discs. It is therefore of interest to use the new model for determining the distribution of residual stresses in thin discs subject to various loading conditions, followed by unloading. This paper presents a solution for the residual stresses and strains in a hollow hyperbolic disc loading by external pressure, followed by unloading.


2000 ◽  
Vol 123 (3) ◽  
pp. 271-281 ◽  
Author(s):  
Anthony P. Parker

Autofrettage is used to introduce advantageous residual stresses into pressure vessels. The Bauschinger effect can produce less compressive residual hoop stresses near the bore than are predicted by “ideal” autofrettage solutions. A recently developed numerical analysis procedure is adopted and extended. The ratio of calculated autofrettage pressure (numerical)/ideal autofrettage pressure (Tresca criterion and plane stress) is calculated and verified against available solutions. The case of open-end conditions based upon von Mises and engineering plane strain (constant axial strain with zero net axial force) is examined in detail. The ratio in this case varies between unity and 2/3, but exhibits very significant variations from the plane stress case when the diameter ratio of the tube exceeds 1.8. Results are within 0.5 percent of available analytical, numerical, and experimental results. A simple numerical fit allows all autofrettage pressures to be replicated to within 0.5 percent. The true plane strain pressure ratio is examined and shown to be inappropriate in modeling engineering plane strain. A number of residual hoop and axial stress profiles is presented for radius ratio 2.0. Calculated pressures are used to determine residual hoop stress values for tube diameter ratios from 1.1 to 3.0 for the full range of percentage overstrain levels. These comparisons indicate that Bauschinger effect is evident when the ratio autofrettage radius/bore radius exceeds 1.2, irrespective of diameter ratio. To assist designers the important values of residual hoop stress at the bore are summarized in a composite plot and a numerical fit is provided. The accuracy of the current ASME code using pressure criteria is assessed. The code is shown to be generally and modestly conservative. A design procedure is proposed which appears capable of extending code validity beyond 40 percent overstrain (the limit of the current code) and of eliminating the small nonconservatism at very low overstrain. Hoop strain values are calculated at both the bore and outside diameter of a tube of radius ratio 2 at the peak of the autofrettage cycle using von Mises criterion with open-end, closed-end, and plane strain conditions. These are compared with available solutions; general agreement is demonstrated, with agreement within 2 percent with an accepted simple formula in the case of open ends. ASME code predictions of percentage overstrain based upon strains at the peak of the autofrettage cycle are generally within 6 percent of numerical predictions. This is in turn produces an agreement within approximately 3 percent in residual bore hoop stress calculation. This discrepancy is generally conservative, becoming non-conservative only at overstrain levels exceeding 80 percent. Strain during removal of autofrettage pressure, in the presence of Bauschinger effect, is also calculated. This shows that the difference in strain during the unloading phase is up to 8 percent (ID) and 6.3 percent (OD) compared with the predictions of elastic unloading. These latter results show similar agreement with the ASME code as in the peak-strain analysis and permit correction of estimates of percentage overstrain based upon permanent bore enlargement.


Author(s):  
Wolf Reinhardt

An equivalent solid based method of predicting the plastic (limit) collapse of perforated plates has been developed in the recent literature. Higher order collapse surfaces with suitable symmetry properties are used for the analysis. The equation for the collapse surface contains a number of constants that are determined by comparison to a Finite Element analysis of an actual perforated periodic cell subject to selected membrane states of stress. Using a typical triangular perforation pattern, the present paper investigates the effect of simplifying assumptions that were made during the periodic cell analysis on the predicted collapse load of the actual cell geometry. For a finite thickness cell subjected to a membrane state of stress, the collapse load is expected to lie between that of the bounding cases of plane stress and generalised plane strain, which are compared here. The connection between the collapse of a cell subjected to a membrane state of stress and a cell of large thickness in bending is established.


Alloy Digest ◽  
2016 ◽  
Vol 65 (11) ◽  

Abstract Strenx 960MC is a hot-rolled structural steel made for cold forming, with minimum yield strength of 960 MPa (139 ksi) for stronger and lighter structures. This alloy meets or exceeds the requirements of S960MC in EN 10149-2. This datasheet provides information on composition, physical properties, tensile properties, and bend strength. It also includes information on surface qualities as well as forming, machining, and joining. Filing Code: SA-772. Producer or source: SSAB Swedish Steel Inc..


Alloy Digest ◽  
2018 ◽  
Vol 67 (8) ◽  

Abstract Strenx 700 CR is a cold-rolled structural steel with a minimum yield strength of 700 MPa (102 ksi) used to produce stronger and lighter structures. Strenx 700 CR has good cold forming, welding, and cutting performance. This datasheet provides information on composition, physical properties, and tensile properties. It also includes information on surface qualities as well as joining. Filing Code: SA-819. Producer or source: SSAB Swedish Steel Inc..


Alloy Digest ◽  
2018 ◽  
Vol 67 (10) ◽  

Abstract MHZ 340 (mininum yield strength of 340 MPa) is one of a series of microalloyed cold forming steels. This datasheet provides information on composition and tensile properties as well as fatigue. It also includes information on forming and joining. Filing Code: SA-824. Producer or source: ThyssenKrupp Steel Europe AG.


Sign in / Sign up

Export Citation Format

Share Document