Experimental and Numerical Investigation of Void Nucleation in an AlMgSi Alloy
Summary (3 min read)
- A frequently observed problem with the Gurson model is the lack of transferability between different stress states.
- A set of micromechanical parameters determined for one particular stress state does not necessarily apply to other stress states.
- The void shape has previously been shown to have a significant effect on damage evolution [9, 101.
- This effect depends on stress triaxiality, and it was therefore expected t o also be of significance for the transferability problem.
- It was concluded that these effects cannot alone be responsible for the observed lack of transferability.
- FE model of material unit cell containing an isolated elastic particle.
- In current applications of the Gurson model, it is frequently assumed that the voids are either initially present or that they are nucleated upon the attainment of a certain nucleation strain.
- For larger particles, however, many investigations (e.g. [I, 31) have indicated that the stresses a t the particles are determined by the global stress state.
- The main aim of the present work is to investigate whether the adoption of a stress based nucleation model will improve the stress state transferability of micromechanical parameters for the Gurson model.
- In the first part of this paper, the main results of some micromechanical stress analyses of elastic particles surrounded by an elastic-plastic matrix will be given.
2 Micromechanical stress analyses
- In order to evaluate the local stresses around an elastic particle situated in an elastic-plastic matrix, an axisymmetric finite element (FE) model of a representative material element (unit cell) was established.
- The spring elements are introduced in order to control the stress triaxiality.
- In consistency with a common damage mechanics approach, it is convenient to distinguish between local and global quantities.
- In the present work, local quantities within the unit cell will be referred to as micro-quantities.
- Averaged, or global quantities will be denoted meso-quantities.
2.1 Mesoscopic stresses and strains
- The mesoscopic strains are defined as logarithmic strains in the following manner.
2.2 Material descriptions
- Where 8 and 5 are the uniaxial stress and.
- In the analyses reported here, Young's modulus was set to 70 GPa, the yield stress to 260 MPa and the hardening exponent to 0.1.
- The particle was specified as purely elastic with a Young's modulus of 130 GPa and a Poisson's ratio of 0.33.
2.3 Stresses at the particle-matrix interface
- It was found that with an appropriate adjustment of the k,-factor, the Argon model reasonably well predicts the maximum normal stress over the interface.
- For the spheroidal particles, the normalised stresses tended to vary more with the strain level than was the case for the spherical particle.
2.4 Stresses in the particle cross-section
- Experimental investigations of void nucleation from second-phase particles and inclusions often show an increased tendency for particle fracture with increasing particle aspect ratio (e.g. ).
- -matrix interfacial stress can be evaluated Although the ratio increases with increasing particle aspect ratio for all stress triaxialities, the increase is too small t o be any major explanation to the abovementioned observations.
3 Simulation of ductile fracture in axisymmetric tensile specimens
- In order to investigate the effects of using a stress controlled nucleation model, detailed simulations of smooth and notched axisymmetric tensile specimens were performed.
- Similar specimens of an AlMgSi alloy have previously been tested experimentally, thus allowing for a determination of micromechanical parameters for this alloy.
- It has been shown [Ill that the nucleation phase in aluminium alloys may constitute the major part of the total ductility.
3.1.1 Material description
- The test material was taken from an extruded AlMgSi alloy.
- Chemical composition is shown in table 1. Metallographical investigations  revealed that the only constituent particles were AlFeSi.
- These particles were oriented with their longitudinal axes in the direction of extrusion and had an average aspect ratio of about 2.7.
3.1.2 Mechanical behaviour
- Three specimens of each geometry were tested but the variation in mechanical response among the parallels was negligible.
- The smooth specimens were also provided with an extensiometer for more accurate recordings of displacements.
- These recordings were used for establishing a 'true' stress-strain curve, see Figure 4 .
3.2 Numerical calculations
- The Gurson model was implemented through the UMAT user subroutine in ABAQUS.
3.2.1 Nucleation model
- Using a purely stress-controlled nucletion model may lead to some numerical difficulties.
- These are mainly attributable to the general softening effect of cavitation, i.e. a increment in porosity may give a negative increment in effective stress.
- The nucleation strain E N is computed separately for each point in the specimens according to the actual stress state.
- In order to include the lower 'half' of the normal distribution in equation ( 12), it is necessary to know the nucleation strain before the analysis actually reaches that strain.
- At the beginning of each increment, the matrix flow stress corresponding to a 'trial' strain equal to the current plastic strain plus 3SN is determined.
3.2.2 Void growth
- The nucleation process as well as the early stages of void growth are very complex.
- Large parts of the broken particles may remain bonded to the matrix and probably alter the growth pattern.
- Since these aspects are not known, it was decided not to include the influence of void shape in the present investigation.
3.2.3 Void coalescence
- By letting the void coalescence be a 'natural' consequence of the damage evolution, the calibration of micromechanical parameters can be based on the nucleation parameters rather than the coalescence parameters.
- In this way it is believed that more 'realistic' parameters can be established and thereby improve the chances of obtaining parameters that are stress state independent.
- As could be expected, the incipient void nucleation starts a t a much higher strain level for the smooth specimen than for the three other specimen geometries.
- Looking a t Figure 5 , one may be led to the conclusion that the same results could have been obtained with a constant nucleation strain of about 5%.
- With a constant nucleation strain, the damage distribution would have been significantly altered.
- For specimen TSR08, for instance, final failure would have been predicted a t a much earlier stage because the most severely damaged region would then have been in the highly strained (but with relatively low stress triaxiality) region in front of the notch root.
- With an appropriate choice of micromechanical parameters, the Gurson model gives good predictions of ductility for a wide range of stress states.
- An appropriate nucleation model in combination with a micromichanical based coalescence criterion, shows good prospects with respect to the ability to determine physically realistic nucleation parameters.
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Cites methods from "Experimental and Numerical Investig..."
...Søvik (1996) used axisymmetric unit cell with elastic round particle and elasto-plastic matrix, and with spring elements to control stress triaxiality and analyzed the relation between stresses in particles and averaged macrostresses in AlMgSi alloys....
...Nous trouvons aussi certaines incohérences, certains auteurs choisissent N C f f [81, 199, 203, 204], ce qui est incorrect d'un point de vue phénoménologique étant donné que le phénomène de coalescence ne peut précéder la nucléation des cavités....
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