Fracture damage evolution of 7075 ultra-high strength aluminum alloy under uniaxial tension with complex loading paths

Determining the hot forming limits of titanium alloy sheet under different strain paths by constant equivalent strain rate hot gas bulging tests

The effect of complex strain path on the properties of CuSi5 silicon bronze

The current studies of strain paths' effect on the forming limit diagram(FLD) are briefly summed up from 4 aspects, moreover, the concepts that complex, simple stain paths are axplained, and the geometric relationship of varians strains is illustrated which is based on Hill'48 yield criterion, are illustrated. In order to calculate limit strains of sheet metal during it's forming with any complex strain path, the three assumptions for sheet metal forming are proposed, viz. Any complex strain path might be transformed to the broken-line strain paths combined with a number of linear strain paths by simplifying; The limit thickness strain might be equal to sheet metal formability; The formability of sheet metal under the broken-line strain path might be dependent on the final strain ratio in forming process, and the line of reasoning on them is annotated. At the same time, on the basis of these assumptions, the theoretical formulas for calculating limit strains in sheet metal forming are deduced under the broken-line strain path with strains' principle axes turning during alternating from prior strain path to subsequent one, in terms of which the forming limit diagrams could be drawn for sheet metal forming with any complex strain path.

Limit dome height test is commonly used for evaluating the formability of sheet material. Through altering the geometry of specimens, different strain paths could be obtained to establish forming limit diagram of the material. By incorporating finite element analysis with ductile energy criteria, engineers can also predict the formability of material. The forming limit diagram or constants in ductile energy criteria are usually determined by experiments with linear strain path. However, the predictions may lose their accuracy when evaluating products with complex strain paths, which is commonly seen in sheet forming processes. Therefore, a better method for evaluating formability of material under complex strain path should be developed. In this study, novel specimen designs for limit dome height test are applied to generate different strain paths with two-step strain effect on the specimens. Different geometric parameters of the novel specimen design can alter the slope of strain paths and create different strain paths similar to the two-step deformation conditions occurred in actual sheet forming processes. Three different two-step strain path conditions are created experimentally, and the changes in strain path are verified with simulations. From the results, the predictions of forming limit based on linear strain path forming limit diagram could be overestimated or underestimated under two-step strain path conditions. Thus, the formability of material under two-step strain path conditions can be determined by corresponding experiments using novel specimen designs, instead of predictions made by linear strain path conditions.

Stacking fault energy (SFE) plays an important role in face centred cubic (f.c.c.) metals and alloys in determining the prevailing mechanisms of plastic deformation. Low SFE metals and alloys have a tendency to develop mechanical twinning, besides dislocation slip, during plastic deformations. Deformation behaviour and microstructure evolution under simple and complex strain paths were studied in 70/30 brass, with small and intermediate grain sizes, which corresponds to a f.c.c. material with low SFE. Simple (rolling and tension) and complex (tension normal to previous rolling) strain paths were performed. The macroscopic deformation behaviour of materials studied is discussed in terms of equivalent true stress vs. equivalent true strain responses and strain hardening rates normalized by shear modulus (dσ/dε)/G as vs. (σ – σ0)/G (σ0 is the initial yield stress of the material and G is the shear modulus). The mechanical behaviour is discussed with respect to dislocation and twin microstructure evolution developed in both, simple and complex strain paths.

The forming limit diagram (FLD) has been widely used as a measure of the maximum formability of a material in tube hydroforming (THF). The geometric shape of the FLD varies owing to the influences of many factors, especially the strain path. Therefore, discussing the change rule of FLDs under various strain paths has practical significance. In the present study, strain paths generated from THF are classified as simple or complex ones. The FLDs for THF are established based on Swift’s diffused necking criterion and Hill’s localised necking criterion along both simple and complex strain paths. Through a comparison of the FLDs obtained from various strain paths, the influences of changing strain path are revealed. Some THF experiments under various strain paths are performed to verify the theoretical analysis. The theoretical analysis and experimental results prove that the position of the FLD changes with different strain paths. Compared with the FLD position established along a simple strain path, the FLD position under a two-stage linear strain path moves in the upper left direction with an initial uniaxial tensile strain path and in the lower right direction with an initial equibiaxial tensile strain path.

Analysis of plastic flow localization under strain paths changes and its coupling with finite element simulation in sheet metal forming

Ni-based superalloy components with complex shape, such as conical-cylindrical parts, are one of the most important structural components widely used in aviation and aerospace fields. Composite spinning process, consisting of shear spinning and deep drawing spinning, is the most effective method to manufacture this complex component. However, the fracture and wrinkling defects usually occur due to the severe work hardening and complex strain path. Therefore, in order to evaluate the forming limit of Ni-based superalloy during spinning under complex strain path at room temperature, the finite element model of the shear-deep drawing composite spinning was established. The strain path during the shear-deep drawing composite spinning was analysed. The forming limit of Ni-based superalloy was also studied. Then the forming limit diagram of Ni-based superalloy during the shear-deep drawing composite spinning was established. The results show that the limit half cone angle of Ni-based superalloy for shear spinning is 30°; and the limit deep drawing spinning coefficient is 0.63. The strain path can be approximately the superposition of two linear strain paths during shear-deep drawing composite spinning. The safety zone is “wing shaped” in tension-compression strain zone during the shear-deep drawing composite spinning. The experimental results show that the limit diagram can accurately predict the forming defects.

Formability, damage and corrosion resistance of coated steel sheets

On plastic deformation and fatigue under multiaxial loading

Forming limit diagrams (FLDs) in simple and complex deformation paths are determined using a theoretical model of localized necking due to an initial heterogeneity of the sheet. The influence of the strain path upon the formability of the sheet is investigated using different types of FLDs under complex strain paths.The effect of material strain hardening and strain-rate hardening is examined for several strain paths. The influence of the imperfection level on the FLDs is presented. Computer simulation of the evolution of rheological parameters during deformation and their dependence on the strain path is carried out.The model is compared with previous experimental works, and a good agreement is obtained between theoretical results and experimental forming limit diagrams.The mathematical model developed in this work is shown to be a powerful tool to understand and predict the plastic behaviour of metal under simple and complex strain paths.

Various thin-walled parts with fairly complex shapes are produced from sheet metals such as automotive panels and other structural parts. In these processes, damage and fracture may be observed on the work piece, and formability plays a fundamental role. Therefore, determination of forming limits and prediction of rupture modes in these operations is very important for process design engineers. In this paper, first, based on plane stress elasto-plasticity and finite strain theories a fully coupled elastic-plastic-damage model is used to predict damage evolution in one sheet metal forming process with nonlinear and complex strain paths. As the plane stress algorithm is valid for thin sheet metals and finite strain theory is recommended for large deformations or rotations, the model is able to quickly predict both deformation and damage behaviour of the parts with nonlinear and complex strain paths. The numerical simulations are compared with experimental tests. Comparison of the numerical and experimental results shows that the proposed damage model is accurate for various forming conditions. Hence, it is concluded that finite element method combined with continuum damage mechanics, can be used as a reliable and rapid tool to predict damage evolution in sheet metal forming processes with nonlinear and complex strain paths.

Investigations of the effect of strain path changes on forming limit curves using an in-plane biaxial tensile test

Metastable austenitic stainless steels are used in many applications, from shavers and kitchen sinks to various applications in the food industry. The diversity in applications of this type of steels is possible due to the many positive properties of the steel. It is not only esthetically pleasing, it also has a good corrosive and wear resistance, it is easy to clean and it does not support biofilm growth as well as other steels. Besides the benefits of using austenitic stainless steels in products, also some benefits can be found during the production of the products: these types of steel are easily deformable, but also have a high strength. These contradicting properties can both be found in the steel because of a phase change occurring during deformation. The austenitic phase, which is soft and easily deformable, can transform into the martensite phase, which is harder and less deformable compared to the austenite. Accompanying the transformation is a transformation strain, witch improves the deformability of the steel even further. A downside of the steel is the complex material behavior and the complicated modeling of this behavior. Models of production processes are often used to determine the optimal process conditions to obtain the desired dimensions, mechanical properties and the lowest cost price of a product. The accuracy of these models depends greatly on the accuracy of the material model describing the deformation process of the steel. The development of an accurate model describing the deformation of a metastable austenitic stainless steel is not easily done. While several models exist which can describe various, relatively straight forward proportional experiments performed on austenitic steels, none can describe the correct behavior of the steel at more complex strain paths, which commonly occur during the production of a product. Two examples of areas in which the current models need to be improved are the relation between the transformation behavior of the steel, preferred orientations of the austenite grains –texture– and the strain direction as well as the influence of a changing strain path –non-proportional strain– on the transformation. These effects cannot be observed during standard experiments used to determine the parameters for the currently existing material models, but do occur during the deformation process of a product. In this research these effects on transformation of austenitic stainless steels were investigated. The results from this research can be used to develop new, more accurate material models. The material behavior during the deformation in various directions of two metastable austenitic stainless steels, one with and one without a crystallographic texture, were investigated. Both steels show transformation during deformation, but while transformation in the textured material dependeds on the deformation direction, in the untextured steel it does not. Investigating the austenitic texture after deformation and transformation shows that the orientation of an austenite grain with respect to the stress has a strong influence on the transformation properties of the grain. Several models are presented which can predict this behavior. The influence of a non-monotonic strain path on the transformation is studied by applying various subsequent strain paths on a steel specimen. In this research, most attention has been paid on a strain path containing a strain reversal. It is shown that, besides the classical Bauschinger effect –the decrease in flow stress after a load reversal–, also the transformation behavior, and thus the material behavior, changes significantly after the strain reversal. The similar effect has been observed during non-proportional strain paths. This research shows that the current material models describing the material behavior of metastable austenitic stainless steels during deformation, can be improved. Based on the knowledge obtained during this research, it is possible to develop new models capable of describing the material behavior during 3- dimensional deformation processes more accurately.

Strain path and work-hardening behavior of brass