(1) A domain where the cleavage fracture initiation is possible to occur is defined as an active zone.
(2) The active zone is divided by cubic volume elements of the same size. A schematic view of the active zone and volume element is shown in Fig. 3.
(3) Ferrite grains are assigned at random in each volume ele
ment based on ferrite grain size distribution until sum
of the volumes of assigned grains reaches the elemental volume. Crystallographic orientation of each grain is deter
mined at random at the same time.
(4) Cementite particles are assigned in each volume element
based on cementite particle thickness (minor axis) distribution. The shape of the cementite is approximated as a prolate spheroid.
(5) Stress tensor and equivalent plastic strain at each volume element are evaluated by macroscopic elasto-plastic FEA using true stress-strain curve.
(6) In a calculation, step time increments are defined. And then, the cleavage fracture initiation process based onthe three stages is evaluated in each volume element for each time step as
following (viii) ~ ().
(7) For Stage I, cracked cementite particle distribution is evaluated based on Eqs. (1) and (2) by using the distribution of cementite particle thickness in the volume element.
(8) For Stage II, first, two ferrite grains (Grain A and Grain B) next to the respective cracked cementite obtained in (8) are selected at random. Grain A and Grain B are used for the evaluation of in Eq. (4) and in Eq.
(5), respectively. Assuming the location of the each cementite particle on the boundary of Grain B, the length of dislocation line is determined. Then, the fracture condition of Stage II is evaluated based on Eq. (3) for all
the combinations of the ferrite grains and the cracked cementite particles. If the fracture condition is satisfied, acleavage crack forms in Grain A and the cleaved grain is excluded in following time steps.
(9) In the case that Stage II is satisfied, Stage III is then evaluated based on Eq. (7). in Eq. (8) is calculated by
using the size and direction of the cleavage crack formed in Grain A.
(10) Cleavage fracture is assumed to be initiated at the time whe
n the fracture condition of Stage III is satisfied in any one of the volume elements. That is a “weakest link” assumption in this model.
(11) If the fracture is not initiated, the procedures of (vii) ~ (x) are carried out for the next time step.
(1) A domain where the cleavage fracture initiation is possible to occur is defined as an active zone. (2) The active zone is divided by cubic volume elements of the same size. A schematic view of the active zone and volume element is shown in Fig. 3.(3) Ferrite grains are assigned at random in each volume element based on ferrite grain size distribution until sum of the volumes of assigned grains reaches the elemental volume. Crystallographic orientation of each grain is determined at random at the same time. (4) Cementite particles are assigned in each volume elementbased on cementite particle thickness (minor axis) distribution. The shape of the cementite is approximated as a prolate spheroid. (5) Stress tensor and equivalent plastic strain at each volume element are evaluated by macroscopic elasto-plastic FEA using true stress-strain curve. (6) In a calculation, step time increments are defined. And then, the cleavage fracture initiation process based onthe three stages is evaluated in each volume element for each time step asfollowing (viii) ~ (). (7) For Stage I, cracked cementite particle distribution is evaluated based on Eqs. (1) and (2) by using the distribution of cementite particle thickness in the volume element. (8) For Stage II, first, two ferrite grains (Grain A and Grain B) next to the respective cracked cementite obtained in (8) are selected at random. Grain A and Grain B are used for the evaluation of in Eq. (4) and in Eq.(5), respectively. Assuming the location of the each cementite particle on the boundary of Grain B, the length of dislocation line is determined. Then, the fracture condition of Stage II is evaluated based on Eq. (3) for allthe combinations of the ferrite grains and the cracked cementite particles. If the fracture condition is satisfied, acleavage crack forms in Grain A and the cleaved grain is excluded in following time steps. (9) In the case that Stage II is satisfied, Stage III is then evaluated based on Eq. (7). in Eq. (8) is calculated byusing the size and direction of the cleavage crack formed in Grain A. (10) Cleavage fracture is assumed to be initiated at the time when the fracture condition of Stage III is satisfied in any one of the volume elements. That is a “weakest link” assumption in this model. (11) If the fracture is not initiated, the procedures of (vii) ~ (x) are carried out for the next time step.
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