Micromechanical Simulation of Initiation and Propagation of Cleavage Cracks in the Ductile-brittle Transition Region


Dr. Ngoc Anh Giang

Project manager

Dr. Geralf Hütter


With decreasing temperature typical engineering materials like the most steels become more and more brittle. The reason is the transition of the microscopic failure mode from ductile growth of micro-voids to transgranular cleavage of grains. The drop of the macroscopic fracture toughness caused by the transition from the ductile to the brittle mechanism is a severe problem in engineering applications of body-centered cubic metals since crack-like defects formed during manufacturing or in operation may reduce strength and life-time of a component significantly. In the ductile-brittle transition region the measured fracture toughness values of single crystals and poly-crystals differ by several orders. To the knowledge of the authors no model can explain this discrepancy yet. It is the aim of the present research project to contribute significantly to the understanding of this phenomenon. For this purpose a micromechanical FEM model shall be developed which resolves the microstructure of a ferritic steel at the crack tip discretely in form of particles (segregations, inclusions) and grains. Within different stages of extension of the model the effects of the relevant submechanisms like debonding of particles, fracture of particles, dislocation pile-up at grain boundaries and particles and incompatibility of cleavage planes of neighboring grains shall be investigated and quantified. On this basis the microstructure shall be optimized to increase the fracture toughness.


Firstly, the cleavage initiating carbide particles were resolved discretely in the fracture process zone of a 3D FEM model without considering the grain boundaries.

Micromechanical Model of the Fracture Process ZonePotential fracture or decohesion of the particles or cleavage of the embedding ferritic matrix were modelled by cohesive zones. The performed simulations show, that the increasing plastic yield stress with decreasing temperature triggers cleavage. Furthermore, the competing mechanisms of fracture and decohesion of the carbide particles are recovered in correctly in dependence of temperature. A parameter studiy showed, that the strength of the particles and of the interface between matrix and particles has a different influence in the ductile-brittle transition regime than in the purely ductile regime. Competing MechanismsIn the ductile regime, a maximum fracture toughness is attained if the particles debond early and thus act as sources of voids. In contrast, stronger particles lead to a shift of the ductile-brittle transition temperature towards lower values. I. e. for a given temperature, stronger particles particles lead to a higher fracture toughness in the ductile-brittle transition regime. In order to obtain realistic predictions with this model, the cleavage fracture strength of the metallic matrix must be selected as an adjustment parameter in the range of four times the value of the plastic yield stress. This value is well below the theoretical cleavage fracture strength, since the excessive stress caused by dislocation pile-up at grain boundaries is not taken into account in this model.

In order to take into account the pile-up of dislocations at grain boundaries, a so-called effective gradient plasticity model was used in the next step to describe the deformation behavior of the matrix in a unit cell modeUnit cell model of cleavage initiation at grain boundariesl of. The effective gradient plasticity model could be efficiently implemented in a commercial finite element system using the mathematical analogy to the heat conduction equation. It was initially used in unit cell models to investigate the interaction between carbide particles and grain boundary for the initiation of microcracks. It turned out that this model predicts a multi-stage mechanism as observed experimentally: a micro-crack initiates at a grain boundary and initially grows in the direction of the closest particle, which breaks or debonds, depending on its strength. As soon as the first grain is completely broken, the crack grows into the neighboring grain and shortly thereafter becomes unstable. Sensitivity studies showed that elliptical particles at grain boundaries are most susceptible to crack initiation. The stress level at the grain boundaries reaches the theoretical cleavage fracture strength.

The model validated in this way was then used to model the processes in the fracture process zone. Here, an idealized regular grain arrangement was Cleavage initiation at grain boundarychosen in order to utilize the symmetries in the finite element model and thus keep the computational effort handleable. Using the theoretical clevage fracture strength, realistic predictions could be made with this model, both with regard to the qualitative mechanism and the quantitative fracture toughness.
Boundary layer model with grain boundaries within fracture process zone

Crack growth with effective  gradient plasticity model


Deutsche Forschungsgemeinschaft 2016-2019, contract HU2279/1