The paper is focused on the process of identifying stress fields from strain fields in the specimen with a hole. The experiment was realized on the specimen with a hole made from anisotropic material. The main attention is paid to the analysis of deformation in the areas of stress (near the hole). That geometry generates a heterogeneous strain field which has been measured during the test using a digital image correlation system. The advantage of using heterogeneous strain fields in the identification procedure is that a complex state of stress-strain can be analyzed at the same time. On the other hand the stress field cannot be directly computed from the test and a suitable identification procedure has to be developed. Here, the virtual fields method (VFM) adapted for plastic strain has been used to identify the hardening behaviour and the anisotropy of the material. The values obtained by the VFM have been compared with the results coming from a standard identification made with uniaxial tensile tests.
In sheet metal forming an anisotropic behaviour of sheet metals is often observed when they undergo plastic deformation. Such anisotropy is due to the rolling process which introduces anisotropy in the texture of the material. The correct identification of the plastic behaviour of anisotropic sheet metal is a very important aspect that has to be taken into account in order to enhance the results of the numerical models.
Traditionally the identification is carried out using uniaxial tensile tests performed at different directions respect to the rolling one. However in recent years, thanks to the development in the full-fields measurement techniques, more complex specimens which generate heterogeneous stress-strain fields can be used to study the behaviour of the material during the plastic flow.
The parameters can be then identified using for instance an inverse approach which includes the finite element (FE) updating [
Another identification procedure is the virtual fields method (VFM) [
The paper is focused on the process of identifying stress fields from strain fields in the specimen with a hole [
The mentioned methods are applied to evaluate the properties of rolled sheets used for automotive production. The uncoated IF steel sheet was used for analysis (interstitial-free (IF)).
This section assesses the properties of cold-rolled sheet metals used in pressing car body parts. A specimen with a hole and the geometry and the dimensions in millimetres as shown in Figure
The geometry and dimensions (mm) of specimen with a hole.
Table
The mechanical properties of the specimen.
Dir. | Thick. |
Rp0,2 |
Rm |
A80 |
|
|
---|---|---|---|---|---|---|
0° | 0,75 | 124 | 297 | 44,5 | 1,7 | 0,25 |
45° | 0,75 | 139 | 305 | 42 | 1,6 | 0,23 |
90° | 0,75 | 132 | 290 | 43,5 | 2,3 | 0,24 |
The specimen was made of DC06 sheet metal of extra deep drawn steel with classic high values of normal anisotropy coefficient
To measure the specimen with a hole, a cross-beam displacement of 0.01 mm/image was set for the first ten steps, a displacement of 0.1 mm/image for the next ten steps, and a displacement of 0.2 mm/image from step 20 until the specimen broke apart (Figure
Diagram of force and cross-beam displacement for specimen with a hole.
The results were visualised for a cross-beam displacement of 3.8 mm using the Vic 3D software.
Figure
The contours of strain fields (a)
Program Camfit is a GUI MATLAB-based software that implements the virtual fields method. It can deal with linear elasticity (isotropic and orthotropic) as well as simple elastoplasticity. Camfit’s purpose is to process the displacement fields measured using the virtual fields method. The theoretical basis of the virtual fields method can be found in the literature [
The values of the displacement fields
For reasons of task symmetry, the area shown along with the grid in Figure
Grid chosen for specimens with a hole.
Figure
The displacement fields
Figure
The strain fields
In elastoplasticity range, Camfit uses only one constant virtual strain field, and as defined in the previous text, it depends on the test configuration. This can also be seen as the difference between averages, normal or shear force, measured and recalculated from the strains, and the constitutive parameters. The program first identifies the isotropic elastic constants (Young’s modulus and Poisson’s ratio) for specimen with a hole, as we can see in Figure
Identification of parameters in elastic area for specimen with a hole.
The second stage concerns the plastic parameters and there are four isotropic hardening models, which are based on the simple Prandtl-Reuss model. In this case, the power law model was chosen and the results are shown in Figure
Parameters obtained in elastoplastic range by Camfit for specimen with a hole.
The values
Comparing the results in figure and those in Table
The parameters obtained by the Camfit program for the elastoplastic area were then processed in Matlab to compute stress fields
The chosen plastic model is the Hill48 yield criterion [
The stress fields obtained from strain fields calculated by Matlab for specimen with a hole for displacement 3.8 mm are illustrated in Figure
The stress fields
Table
Results obtained by Camfit and standardised tensile test.
Camfit | Tensile test | ||||||
---|---|---|---|---|---|---|---|
Parameters in elastic range | Parameters in elastoplastic range (power law) | Yield stress | |||||
|
|
|
|
|
|
Test1 | Test2 |
139,4 | 0,26 | 1284,2 | 0,008 | 0,478 | 125,7 | 124 | 128 |
The present paper is aimed at the process of identifying stress fields from strain fields in the specimen with a hole.
Digital image correlation (DIC) was used to analyze plastic strain development. DIC is one of the rapidly developing modern unconventional optical methods of experimental mechanics. The possibility of overall capture of the displacements on the surface of specimens permits a real picture to be obtained of how strain is distributed at the points of stress.
The material properties of the steel sheet metals used to produce specimens were obtained by standardised tensile tests and their values were compared with the results obtained by an experimental method of identifying sheet metal material properties. Camfit software was used in this experimental method and overall measurement was applied. Comparing the resultant values for the material’s yield point shows a good conformity with the results obtained by Camfit, which uses the virtual work method to make calculations. The Camfit material parameters were then used in determining stress fields using the strain fields measured while applying hardening models suitable for isotropic materials. These methods enable the analysis of stress in the elastic and the plastic areas in tasks of concentrated stress while considering the material’s anisotropy in plastic deformation.
This allows us to predict damage to thin-walled structural features primarily in the areas where stress may concentrate and serves as a basis for assessing the service time of such features and it provides information for the optimisation of the manufacturing of such features by sheet metal cold pressing.
With all responsibility the authors would like to declare that non of them is financially supported by producers or distributors of commercial programmes MATLAB, Camfit, and Vic 3D. Moreover, they do not have any other kind of interest to propagate and support these commercial programmes. In the paper they were used as a necessary tool for their simulations.
This paper has been elaborated in the framework of the project Opportunity for young researchers, reg. no. CZ.1.07/2.3.00/30.0016, supported by Operational Programme Education for Competitiveness and cofinanced by the European Social Fund and the state budget of the Czech Republic and in the framework of the project Regional Materials Technology Research Centre (RMTVC) reg. no. CZ.1.05/2.1.00/01.0040.