Determination of True Stress–Strain Curves of Sheet Metals in Post-Uniform Elongation Range (original) (raw)
Related papers
Accurate stress computation in plane strain tensile tests for sheet metal using experimental data
Journal of Materials Processing Technology, 2010
The advances achieved in phenomenological constitutive laws and their implementation in finite element codes for predicting material behavior during forming processes have motivated the research on material identification parameters in order to ensure prediction accuracy. New models require experimental points describing a bi-axial stress state for proper calibration, and the features of the plane strain tensile test have made it one of the most used. The test's principal inconvenience is the influence of the free edges on strain field homogeneity and stress computation.
Influence of out-of-plane compression stress on limit strains in sheet metals
International Journal of Material Forming
The prediction of the forming limits of sheet metals typically assumes plane stress conditions that are really only valid for open die stamping or processes with negligible out-of-plane stresses. In fact, many industrial sheet metal forming processes lead to significant compressive stresses at the sheet surface, and therefore the effects of the through-thickness stress on the formability of sheet metals cannot be ignored. Moreover, predictions of forming limit curves (FLC) that assume plane stress conditions may not be valid when the forming process involves nonnegligible out-of-plane stresses. For this reason a new model was developed to predict FLC for general, threedimensional stress states. Marciniak and Kuczynski (Int J Mech Sci 9:609-620, 1967) first proposed an analytical method to predict the FLC in 1967, known as the MK method, and this approach has been used for decades to accurately predict FLC for plane stress sheet forming applications. In this work, the conventional MK analysis was extended to include the through-thickness principal stress component (σ 3 ), and its effect on the formability of different grades of sheet metal was investigated in terms of the ratio of the third to the first principal stress components (b ¼ s 3 s 1 = ). The FLC was predicted for plane stress conditions (β=0) as well as cases with different compressive through-thickness stress values (β≠0) in order to study the influence of β on the FLC in three-dimensional stress conditions. An analysis was also carried out to determine how the sensitivity of the FLC prediction to the through-thickness stress component changes with variations in the strain hardening coefficient, in the strain rate sensitivity, in plastic anisotropy, in grain size and in sheet thickness. It was found that the out-of-plane stress always has an effect on the position of the FLC in principal strain space. However, the analysis also showed that among the factors considered in this paper, the strain hardening coefficient has the most significant effect on the dependency of FLC to the through-thickness stress, while the strain rate sensitivity coefficient has the least influence on this sensitivity.
Identification of Strain Hardening Phenomena in Sheet Metal at Large Plastic Strains
Procedia Engineering, 2014
A new experimental/numerical method to identify post-necking strain hardening phenomena in ductile sheet metal is presented. The identification of the post-necking strain hardening behaviour is based on the minimization of the external and the internal work in the necking zone during a tensile test. The proposed method takes the material state and the shape of the whole deforming tensile specimen into account. The post-necking hardening behaviour of a cold rolled interstitial-free steel sheet is identified. A hardening law which enables disentangling pre -and post-necking strain hardening behaviour is presented. The method is experimentally validated using an independent material test. For that purpose, the uniaxial tube expansion test is conducted to obtain uniaxial strain hardening behaviour beyond the point of maximum uniform strain in a tensile test. Finally, the presented method is compared with a hydraulic bulge test.
The Journal of Strain Analysis for Engineering Design, 2020
Ramberg-Osgood (R-O) type stress-strain models are commonly employed during elasto-plastic analysis of metals. Recently, 2-stage and 3-stage R-O variant models have been proposed to replicate stress-strain behavior under large plastic deformation. The complexity of these models increases with the addition of each stage. Moreover, these models have considered deformation till necking only. In this paper, a simplistic multi-stage constitutive model is proposed to capture the strain-hardening non-linearity shown by metals including its post necking behavior. The constitutive parameters of the proposed stress-strain model can be determined using only elastic modulus and yield strength. 3-D digital image correlation was used as an experimental tool for measuring full-field strains on the specimens, which were subsequently utilized to obtain the material parameters. Our constitutive model is demonstrated with an aerospace-grade stainless steel AISI 321 wherein deformation response average...
Journal of Materials Processing Technology, 2017
The determination of the linear elastic modulus is important for the numerical process design of forming operations. Test setups for the identification of the linear elastic modulus can be divided into dynamic methods like ultrasonic measurement and static methods like indentation tests or uniaxial tensile tests. Relevant standards recommend the determination of the linear elastic modulus via linear regression from stress vs. strain curves, while no information for an upper boundary exists. In this contribution, a new approach is presented, which uses the deformation work to identify a materialdependent upper boundary for the determination of the linear elastic modulus. The method is applied to two aluminum alloys AA5182-O and AA6016-T4, a deep drawing steel DX54, two advanced high strength steels HCT600X and HCT980X and a magnesium alloy AZ31B. The results confirmed a robust determination of the linear elastic modulus from the linear elastic behavior and a good reproducibility with a deviation below 5 %. Moreover, with exception of AA5182-O, all investigated materials exhibit a quasi-elastic-plastic (QPE) transition between elastic and plastic material behavior.
Behaviour of Stress Strain Relationship of Few Metals
Journal of Intelligent Mechanics and Automation
The aim of this study is to examine the uniaxial tensile strength of three specimens of mild steel, brass and aluminium is examined. Tension tests enable the determination and prediction of the deformation/deflection response of the material properties and elastic modulus. The values of Young’s Modulus for Elasticity (E) for mild steel, brass, and aluminium have been successfully determined from laboratory experiments. Also, the stress and strain of the materials were graphically shown to have good correlations between theory and experimental values and compositions. The results further show that steel is more suitable for structural application than brass and aluminium respectively, because of their high E Modulus rating. It therefore implies that steel can withstand more tension. The result obtained from the study such as tensile strength, yield strength etc. have been recorded. Also, the related theory has been indicated.
Limit strains in the sheet metals by using the new Hill's yield criterion (1993)
Journal of Materials Processing Technology, 1999
Information upon the formability of thin metal sheets is important for both sheet manufacturers and users. From the producer's point of view, the most signi®cant is the knowledge of the characteristics of the metal sheet correlated to its formability and ability to in¯uence the manufactured process, being able to produce semi-products with previously established properties. From the user's view-point, it is of importance to be able to select the semi-product that allows him to obtain ®nished products of de®nite size and shape at the lowest price possible. More procedures have evolved with time for evaluating metal sheet formability. Some of them are based upon simulative tests, others on mechanical tests. A more realistic and general method has been introduced recently, this being the Forming Limit Diagram (FLD). The present paper presents a new approach to FLD modelling. The yield criterion proposed recently by Hill [R. Hill, Int. J. Mech. Sci. 35 (1993) 19] is used for the calculation of the limit strains in connection with the Swift's instability condition for diffuse necking. # 1999 Elsevier Science S.A. All rights reserved.
A New Method for Correctingthe StressStrain Curves af- ter Bulging in Metals
True stressstrain curve has a basic role in the analysis of deformation in theoretical plasticity and numerical simulations. Because of the triaxial state of stresses in the necking or bulging zones, in tension and the compression tests respectively, the true stressstrain curves obtained from relationsare no longer valid and must be corrected. Various correction techniques have been proposed and can be found in literatures. In this study, a new semi-analytical approach for correction of the stressstrain curve in compression test for circular cross-section specimens was introduced and a relation for the correction factor was derived based on the theory of plasticity. This relation requires only a few experimental surface strain measurements which can easily be done using an image processing technique. The correction factor formula was obtained in terms of the initial radius of specimen, the bulge radius, and the surface strain on the bulge surface. The proposed approach in this study was compared with the results of the numerical simulations. Simulation was used to correct the stress-strain curve based on the optimization method with comparing the bulging profile of tested samples and ones simulated by using genetic algorithm. Nomenclature
Stretching limits in sheet metals: In-plane versus out-of-plane deformation
Metallurgical Transactions, 1974
Limiting principal strains were measured by two different techniques of biaxial stretching of sheets, one of which permits free deformation in a flat plane, while the other causes constrained deformation in contact with a rigid or rubber punch. The latter method, which relates well with industrial experience, produces larger limiting strains under identical degrees of biaxiality. A possible explanation is based on the process of instability and strain localization.