# Elastoplasticity of Grey Cast Iron FE-Algorithms and Biaxial Experiments

[Doktorsavhandling]

This thesis focuses on multiaxial elastoplastic behaviour of graphitic grey cast iron with the aim to provide physically appropriate and numerically reliable constitutive relations for use in FE-codes. To achieve this goal, this work is divided into three parts:

Biaxial experiments are performed on thin cruciform specimens. An existing biaxial hydraulic test unit is equipped with new control and data acquisition modules and a fixture to facilitate compressive loading without excessive out of plane displacements. A test series is performed on some 30 specimens subjected to different ratios of loads in two perpendicular in-plane directions. Several tests included load histories resulting in reversed plasticity.

Based on experimentally determined points of initial yielding and hardening behaviour, constitutive equations founded on the classical incremental theory of plasticity are proposed. It is then assumed that the grey cast iron behaves as a continuum due to the randomness of the distribution of graphite flakes in the pearlitic matrix. For biaxial compressive loadings the material response is governed by the pearlitic matrix, thus resembling the behaviour of many ordinary steels. Yielding in compression is therefore described with a von Mises yield function together with the yield strength, sc, in uniaxial compression. Recorded stress-strain curves in biaxial tension or in tension-compression are found to be more nonlinear with global nonelastic strains observed at very low stress levels. This is explained by severe notch effects of the graphite flakes and the resulting formation of voids and microcracks. The nonelastic strains are here treated as plastic strains (time independent), and yielding is modelled with a von Mises yield function with a term proportional to the first invariant of the stress tensor, I1 = skk, added. This, so-called, modified von Mises yield condition employs two yield stresses, sc, as mentioned above, and the yield stress sT in uniaxial tension which is initially chosen as sT = sc/3. The hardening behaviour is modelled by linear isotropic hardening or linear Prager kinematic hardening. In both cases different hardening parameters in tension and compression are employed. Associated and non-associated flow rules are evaluated.

The kinematic hardening rule together with an associated flow rule is found to give the best agreement with experimental results involving reversed plasticity. For cyclic loadings a kinematic hardening model with multi-linear hardening in tension is proposed.

The constitutive equations proposed are implemented into the commercially available FE-code ABAQUS, through a user-supplied material routine. An operator-split algorithm (elastic predictor, plastic corrector) in combination with a consistent tangent modulus is used for the integration of the constitutive relation proposed.

As an application, a fully three-dimensional study of a cylinder head made of grey cast iron for a heavy duty Diesel truck engine is performed. The cylinder head is subjected to thermal and mechanical loads simulating normal operating conditions. Both the temperature field and the strain and stress fields are calculated using the FE-code ABAQUS.

**Nyckelord: **multiaxial elastoplastic behaviour, graphitic grey cast iron, FE-codes, Biaxial experiments, graphite flakes, hardening behaviour

Denna post skapades 2006-09-19. Senast ändrad 2013-09-25.

CPL Pubid: 1481