Study On The Determination Of Hardening Curve In Large Range Of Strains From Tensile Tests For Ductile Metals

With the rapid development of numerical simulation technologies,finite element analysis(FEA)has been increasingly adopted to cope with various kinds of problems related to plastic forming.With the help of FEA,people can understand the flow behaviors during the plastic forming process of metal materials more deeply,determine the critical state of instability and fracture more easily,and finally achieve the prediction of forming quality in a rapid,accurate and low-cost way,which can be used to guide the modern plastic precision forming processes.The reliability of the results predicted by FEA depends on the accuracy of the input material constitutive models directly,where the hardening curve plays a decisive role.Not only the accuracy of hardening curve dominates the precision of FEA,but also the strain range covered by the hardening curve corresponds to the maximum deformation level that can be achieved in FEA.In the actual forming process like forging and stamping,the part often experience large degrees of plastic deformation,the strain even exceeds 1.0.Correspondingly,the hardening curve input into FEA is required to have a correspondingly large strain range.Currently,uniaxial tension test is the most widely used method for determining the hardening curve of metal materials.However,the uniform strain range achieved by the traditional uniaxial tension test does not exceed 0.3 generally,which cannot meet the requirement of actual forming prediction under large plastic deformation.Ductile metal materials generally experience significant plastic strain in the post-necking stage.However,due to the localized deformation of specimen in the necking region,the stress state does not maintain uniaxial any longer,resulting in the calculation of post-necking stress and strain becoming extremely difficult.For this reason,researchers have proposed several methods for determining the hardening curve in large range of strains from uniaxial tension test.These methods are different from each other and can be classified into three main categories in the introduction of this study: 1)direct calculation method;2)inverse identification method;3)pre-strained multi-specimen method.In the actual application of these methods,all of them have varied degrees of limitations.At present,regarding the determination of hardening curve in large range of strains from uniaxial tension test,there are still many questions that need to be answered urgently.For example,how about the versatility of these methods,what are the reasons resulting in the measurement errors,what are the main influencing factors of the measurement accuracy and how to improve the measurement accuracy of these methods,etc.Based on the mentioned above,this study aims at determining the hardening curve in large range of strains from uniaxial tension test accurately.To achieve the final goal,direct calculation method,inverse identification method as well as pre-strained multi-specimen method were studied.In view of the limitations of these existing methods,based on the theoretical analysis of influencing factors,corresponding innovative solutions were proposed to improve the accuracy and enlarge the strain range of the determined hardening curve,simultaneously.Finally,based on the analysis and comparison of the measurement accuracy and strain range for different methods,an attempt was made to establish a theoretical specification and measurement system for determining the hardening curve in large range of strains from uniaxial tension test.Ductile metal materials including Q460 steel bar and H300LAD+Z steel sheet were used as experimental materials in this study.The research works and main conclusions are summarized as follows:(1)The simulations of uniaxial tension test using reference material models with different hardening behaviors were conducted.The error origins of the existing direct calculation methods based on contour measurement(Bridgman,Siebel and Chen)were clarified,i.e.the two assumptions in the minimum cross section of necking including the uniform distribution of strain and the equal relationship between radial strain and hoop strain are not valid in large range of strains.The errors of these existing methods increase with the increase of the normalized necking radius of minimum cross section((6/(6?),and its increase trend is associated with material strain hardening exponent n.Therefore,considering (6/(6? and n simultaneously,the corresponding modified methods were proposed and applied to Q460.The strain range of hardening curve for modified method is about 0?0.98,which is 29 times of the uniform strain range(0?0.033)before necking determined by conventional tension test,indicating the strain range that can be achieved by the conventional tension test for metal bars were improved significantly.By comparing with the inversely identified hardening curve,corresponding to the plastic strain of 0.98,the maximum errors of modified methods are 1.5%,1.2% and 2.5% respectively,which are less than that of original method(9.5%?8.5% and 10.4%),proving that the modified methods have an obvious improvement on determining post-necking hardening curve for cylindrical specimen.(2)Due to the initial anisotropy of sheet metal and the geometric complexity of its tensile necking,the direct calculation of post-necking hardening curve for sheet metal is very difficult.To this end,a direct calculation method based on strain measurement for determining the postnecking hardening curve for sheet metals was proposed.Firstly,the local strain fields of necking region captured by digital image correlation(DIC)were used to determine the average true stress vs.strain curve.Considering the stress state of diffusion necking maintains plane stress state,the correction methods for equivalent stress and strain during diffusion necking were derived by using the combation of anisotropic yield criterions(Hill48 and Yld2000-2d)and flow rules(associated and non-associated).The strain range(0?0.85)covered by the hardening curve of H300LAD+Z sheet determined by the proposed method is 5.7 times of the uniform strain range(0?0.15)before necking determined by conventional tension test,proving the proposed method can determine the post-necking hardening curve for sheet metal.The determined hardening curve was adopted in the simulation of uniaxial tension test for sheet specimen,the simulated load vs.displacement curve matches well with the experimental one,proving the high accuracy of the proposed method.For the uniaxial tension test of sheet metals,the proposed method can be adopted as a specification for determining the postnecking hardening curve.(3)Considering the existing inverse methods have limitations of cumbersome calculation and low effectiveness on the determination of post-necking hardening curve,the comprehensive inverse identification strategy considering the combinations of setting initial values,designing optimization ranges and using approximate model was proposed in this study.For cylindrical tension specimen,by measuring the cross-sectional diameter of fractured specimen,the initial values of flow stress and plastic strain at fracture moment can be determined via Leroy-Bridgman formula,which can provide a rather accurate starting value for the subsequent process of fitting the parameters of hardening model,experimental deisgn and parameters optimization.Moreover,considering the error range of Leroy-Bridgman formula,the optimization range for the hardening parameters to be identified can be given.For flat tension specimen,considering the change of stress state after necking,the average true stress vs.true strain curve measured by DIC was used as the upper limit of hardening curve optimization.Moreover,considering the strain hardening behaviors of metal materials,the flow stress st the previous strain moment can be regarded as the lower limit of current flow stress.The results show that the starting values and the variation range of parameters to be inversely identified can be determined effectively through the proposed comprehensive inverse identification strategy.The inverse identification of hardening curve in large range of strains from tension test can be realized by using 20 simulations and 9 iterations for Q460 and H300LAD+Z,respectively,proving the high effency of the proposed comprehensive inverse identification strategy.The strain range covered by the inversely identified hardening curve are 0?1.0 and 0?0.9,which are far larger than the uniform strain range(0?0.033 and 0?0.15)before necking determined by conventional tension test.The inversely identified hardening curves were applied to the simulations of uniaxial tension test for Q460 and H300LAD+Z,the simulated load vs.displacement curves are coincidence well with the experimental ones,showing the high accuracy of the inversely identified hardening curve.(4)The limitations of the existing pre-strained multi-specimen method in measuring the hardening curve in large range of strains were analyzed and corresponding solutions or modifications were proposed.For metal bars,a pre-torsioned multi-specimen method was proposed,which can solve the problems that the existing multi-specimen methods based on pre-extrusion,pre-drawing and pre-compression generally require the repeated preparation of tensile specimens,having low experimental cost and high measurement efficiency.For sheet metal,the results of FEA have confirmed that the anisotropy of sheet metal has a certain influence on the values of equivalent strain accumulated by the pre-rolling.By considering of the anisotropy of sheet metal,a modified calculation method for the equivalent strain accumulated by pre-rolling was proposed.The proposed two methods were applied to Q460 and H300LAD+Z respectively,their maximum effective strain(?0.6 and ?1.4)are obviously higher than the necking strain of traditional tension test(?0.033 and ?0.15).The hardening curves determined by pre-strained mulyi-specimen method coincide well with the inversely identified hardening curves using single tension specimen,proving the high accuracy of the proposed and modified methods.(5)By comparing and analyzing the direct calculation method,the inverse identification method and the pre-strained multi-specimen method,the measurement specification for the hardening curve in large range of strains from uniaxial tension test was further given.Firstly,in terms of measurement accuracy,the direct calculation methods mainly rely on the accuracy of local geometric information(for metal bar)or strain field information(for metal sheet)at the necking,the inverse identification methods depend on the accuracy of finite element simulation and the rationality of inverse identification strategy,while the pre-strained multispecimen method rely on the accurate measurement and calculation of the pre-strains.Secondly,in terms of the strain range,both the direct calculation methods and the inverse identification methods are limited by the ultimate strain values of necking before tensile fracture,while the pre-strained multi-specimen method depends on the maximum strain values that can be accumulated by the pre-deformation.Finally,in view of the complexity of the plastic constitutive models,only on the premise of obtaining the true characterization of other constitutive relations of the material,such as anisotropic yield and kinematic hardening,etc.,we can obtain a sufficiently accurate hardening curve in large range of strains from uniaxial tension test.To sum up,this study aims at the determination of hardening curve in large range of strains for ductile metals from uniaxial tension test.In view of the limitations of existing methods,a number of innovations and improvements have been proposed from three aspects: direct calculation method,inverse identification method and pre-strained multi-specimen method,which improved the measurement accuracy and expanded the strain ranges.The research works have clarified some theoretical issues and established a rather systematic and complete theoretical specification as well as measurement system.Furthermore,the proposed methods enriched the measurement methods of hardening curve in large range of strains for metal materials,which are beneficial to improve the accuracy of finite element simulations and further promote the development of modern precision plastic forming processes.