Experimental and Numerical Investigation of Void Nucleation in an AlMgSi Alloy
Summary (3 min read)
1 Introduction
- 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.
Particle
- 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.
2.2 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. [2]).
- -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 [7] 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 .
3.2.1 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.
3.2.4 Results
- 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.
4 Conclusions
- 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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