Rakenteiden Mekaniikka, Vol . 25 No 3 1992, ss. 3 - 23 This article studies the basics of fractur... more Rakenteiden Mekaniikka, Vol . 25 No 3 1992, ss. 3 - 23 This article studies the basics of fracture mechanics. The theory proposed by Griffith is derived starting from the examination of the law of kinetic energy. A condition for crack growth is formulated. This equation also contains the influence of kinetic energy and continuum dissipation. The condition is expressed in the rate form i.e . it describes the response of a continuum in the case of a running crack. In the special case, the derived condition reduces to that proposed by Griffith.
Proceedings of the Estonian Academy of Sciences. Engineering, 2002
Gurson-Tvergaard material model has been evaluated by using damage mechanics and thermomechanics.... more Gurson-Tvergaard material model has been evaluated by using damage mechanics and thermomechanics. The evolution law of Tvergaard for the void volume fraction is rigorously derived. It follows that the modification for rate of the void volume fraction by Chu and Tvergaard and Tvergaard and Needleman cannot be accepted since it violates the axiom of conservation of mass. An extension of the Gurson-Tvergaard model has been derived. Using the extended model it has been shown that under compression there are stress states by which the Gurson-Tvergaard material model does not satisfy the Clausius-Duhem inequality.
A material containing spherical microvoids with a Hookean matrix response was shown to take the a... more A material containing spherical microvoids with a Hookean matrix response was shown to take the appearance usually applied in continuum damage mechanics. However, the commonly used variable damage D was replaced with the void volume fraction f , which has a clear physical meaning, and the elastic strain tensor \Bold {ε}^e with the damage-elastic strain tensor \Bold {ε}^{de}. The postulate of strain equivalence with the effective stress concept was reformulated and applied to a case where the response of the matrix obeys Hooke’s law. In contrast to many other studies, in the derived relation between the effective stress tensor \Bold {\Tilde{σ}} and the stress tensor \Bold {σ}, the tensor \Bold {\Tilde{σ}} is symmetric. A uniaxial bar model was introduce for clarifying the derived results. Other candidates for damage were demonstrated by studying the effect of carbide coarsening on creep rate.
A material model is presented that includes the following deformation mechanisms: the instantaneo... more A material model is presented that includes the following deformation mechanisms: the instantaneous response of ice due to distortion of crystal lattices, creep, the formation of microcrack nuclei due to creep, the formation of microcracks, and deformation due to microcracks. The new material model has a strict foundation on deformation mechanisms. This constitutive equation was applied to sea ice for engineering applications through implementation in the Abaqus explicit code by writing a VUMAT subroutine. The computed results show that the model correctly predicts the uniaxial tensile and the uniaxial compressive strengths of ice. The computed compressive strength versus strain-rate relation takes an almost linear relation when expressed in the log–log coordinates, which fits well with the data obtained from the literature. The material model shows the Hall–Petch type of strength dependency on the grain size.
Derivation of the normality rule for time-dependent deformation by the principle of the maximal r... more Derivation of the normality rule for time-dependent deformation by the principle of the maximal rate of entropy production was carried out. The derivation was made within the framework of thermomechanics with internal variables. Since Ziegler did not cast his principle into an exact mathematical framework, it was done here. A condition for the multiplier in the normality rule (c.f. plasticity multiplier) was derived. If the condition gives a constant value for the multiplier, the specific (complementary) dissipation function was shown to be a homogeneous function. In the case where the value of the multiplier depends on the state variables, the dissipation potential is a non-homogeneous function.
Journal of the Mechanical Behavior of Materials, 2000
The Gurson-Tvergaard material model was studied from the basic laws of thermomechanics point of v... more The Gurson-Tvergaard material model was studied from the basic laws of thermomechanics point of view. The model was successfully used for prediction of crack growth in fracture mechanics specimens of various materials used in nuclear reactor pressure vessels. Theoretical evaluation of the model showed that when the hydrostatic part of the stress is compression there are states which do not satisfy the second law of thermodynamics. The evolution equation for void volume fraction f applied by Tvergaard and Needleman is in contradiction of the continuity equation.
Rakenteiden Mekaniikka, Vol . 25 No 3 1992, ss. 3 - 23 This article studies the basics of fractur... more Rakenteiden Mekaniikka, Vol . 25 No 3 1992, ss. 3 - 23 This article studies the basics of fracture mechanics. The theory proposed by Griffith is derived starting from the examination of the law of kinetic energy. A condition for crack growth is formulated. This equation also contains the influence of kinetic energy and continuum dissipation. The condition is expressed in the rate form i.e . it describes the response of a continuum in the case of a running crack. In the special case, the derived condition reduces to that proposed by Griffith.
Proceedings of the Estonian Academy of Sciences. Engineering, 2002
Gurson-Tvergaard material model has been evaluated by using damage mechanics and thermomechanics.... more Gurson-Tvergaard material model has been evaluated by using damage mechanics and thermomechanics. The evolution law of Tvergaard for the void volume fraction is rigorously derived. It follows that the modification for rate of the void volume fraction by Chu and Tvergaard and Tvergaard and Needleman cannot be accepted since it violates the axiom of conservation of mass. An extension of the Gurson-Tvergaard model has been derived. Using the extended model it has been shown that under compression there are stress states by which the Gurson-Tvergaard material model does not satisfy the Clausius-Duhem inequality.
A material containing spherical microvoids with a Hookean matrix response was shown to take the a... more A material containing spherical microvoids with a Hookean matrix response was shown to take the appearance usually applied in continuum damage mechanics. However, the commonly used variable damage D was replaced with the void volume fraction f , which has a clear physical meaning, and the elastic strain tensor \Bold {ε}^e with the damage-elastic strain tensor \Bold {ε}^{de}. The postulate of strain equivalence with the effective stress concept was reformulated and applied to a case where the response of the matrix obeys Hooke’s law. In contrast to many other studies, in the derived relation between the effective stress tensor \Bold {\Tilde{σ}} and the stress tensor \Bold {σ}, the tensor \Bold {\Tilde{σ}} is symmetric. A uniaxial bar model was introduce for clarifying the derived results. Other candidates for damage were demonstrated by studying the effect of carbide coarsening on creep rate.
A material model is presented that includes the following deformation mechanisms: the instantaneo... more A material model is presented that includes the following deformation mechanisms: the instantaneous response of ice due to distortion of crystal lattices, creep, the formation of microcrack nuclei due to creep, the formation of microcracks, and deformation due to microcracks. The new material model has a strict foundation on deformation mechanisms. This constitutive equation was applied to sea ice for engineering applications through implementation in the Abaqus explicit code by writing a VUMAT subroutine. The computed results show that the model correctly predicts the uniaxial tensile and the uniaxial compressive strengths of ice. The computed compressive strength versus strain-rate relation takes an almost linear relation when expressed in the log–log coordinates, which fits well with the data obtained from the literature. The material model shows the Hall–Petch type of strength dependency on the grain size.
Derivation of the normality rule for time-dependent deformation by the principle of the maximal r... more Derivation of the normality rule for time-dependent deformation by the principle of the maximal rate of entropy production was carried out. The derivation was made within the framework of thermomechanics with internal variables. Since Ziegler did not cast his principle into an exact mathematical framework, it was done here. A condition for the multiplier in the normality rule (c.f. plasticity multiplier) was derived. If the condition gives a constant value for the multiplier, the specific (complementary) dissipation function was shown to be a homogeneous function. In the case where the value of the multiplier depends on the state variables, the dissipation potential is a non-homogeneous function.
Journal of the Mechanical Behavior of Materials, 2000
The Gurson-Tvergaard material model was studied from the basic laws of thermomechanics point of v... more The Gurson-Tvergaard material model was studied from the basic laws of thermomechanics point of view. The model was successfully used for prediction of crack growth in fracture mechanics specimens of various materials used in nuclear reactor pressure vessels. Theoretical evaluation of the model showed that when the hydrostatic part of the stress is compression there are states which do not satisfy the second law of thermodynamics. The evolution equation for void volume fraction f applied by Tvergaard and Needleman is in contradiction of the continuity equation.
Uploads
Papers by Kari Santaoja