Thermodynamic Formulation of a Material Model for Microcracking Applied to Creep Damage

Santaoja, Kari

doi:10.1016/j.mspro.2014.06.192

Cited by 3 publications

(4 citation statements)

References 4 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A similar partition is obtained for rectilinear microcracks in a two-dimensional body [12] and for penny-shaped microcracks in a three-dimensional body [30]. Based on Equations (11) and (14) where is the elastic strain tensor, is the damage strain tensor, is the ε e ε d ε sw porosity swelling strain tensor and is the inelastic strain tensor. Equations (17) ε i and (18) 1 give It is worth noting that Expression (18) does not include models for all potential deformation mechanisms.…”

Section: Spherical Microvoids With the Hookean Matrix Responsementioning

confidence: 86%

“…Model (37) 2 is valid for a Hookean matrix deformation with spherical microvoids [see Equation (20)]. According to Santaoja [11,30,36], it is valid for a Hookean matrix deformation with penny-shaped microcracks and for rectilinear microcracks in a 2D solid [12], although for these latter two cases the damage strain tensor has to be made symmetric. Therefore, Equations (38) are valid for g d these three types of material behaviours.…”

Section: Analytical Relation Between the Stress Tensors σ And σ For Tmentioning

confidence: 99%

“…ε de If there is progressive damage evolution in terms of straining of the material, the stress vs damage-elastic strain may take on a dependence as shown in σ ε de Figure 2(a) and be copied with ingredients into Figure 3(a). Expression (11) shows that the effective compliance tensor takes increasing values with increasing S( f ) value for the void volume fraction . Thus, Expression (37) 2 gives the form shown f in Figure 2 Now, the damage is assumed to be due to the microcracks.…”

Section: Analytical Relation Between the Stress Tensors σ And σ For Tmentioning

confidence: 99%

“…It can be a scalar, vector or tensor of any order. Instead of the variable , it is preferable to introduce variables that are connected to the microstructure D of the material, such as the void volume fraction , which is the topic of this f paper, and the microcrack densities introduced by Santaoja [11], [12]. Both the Q r void volume fraction and microcrack densities enter into the theory of f Q r continuum thermodynamics as internal variables, being thus a vital part of continuum thermodynamics.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

On continuum damage mechanics

Santaoja

2019

RakMek

View full text Add to dashboard Cite

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 was replaced with the void volume fraction , D f which has a clear physical meaning, and the elastic strain tensor with the damage-elastic g e strain tensor. The postulate of strain equivalence with the effective stress concept was g de 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 and the stress tensor , the tensor is symmetric. A uniaxial bar model σ σσ was introduce for clarifying the derived results. Other candidates for damage were demonstrated by studying the effect of carbide coarsening on creep rate.

show abstract

Section: Spherical Microvoids With the Hookean Matrix Responsementioning

confidence: 86%

Section: Analytical Relation Between the Stress Tensors σ And σ For Tmentioning

confidence: 99%

Section: Analytical Relation Between the Stress Tensors σ And σ For Tmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

On continuum damage mechanics

Santaoja

2019

RakMek

View full text Add to dashboard Cite

show abstract

A complete three-dimensional continuum model of wing-crack growth in granular brittle solids

Kolari

2017

International Journal of Solids and Structures

View full text Add to dashboard Cite

Material Model for Creep-Assisted Microcracking Applied to S2 Sea Ice

Santaoja

Reddy

2016

Journal of Applied Mechanics

View full text Add to dashboard Cite

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.

show abstract

Thermodynamic Formulation of a Material Model for Microcracking Applied to Creep Damage

Cited by 3 publications

References 4 publications

On continuum damage mechanics

On continuum damage mechanics

A complete three-dimensional continuum model of wing-crack growth in granular brittle solids

Material Model for Creep-Assisted Microcracking Applied to S2 Sea Ice

Contact Info

Product

Resources

About