Speakers
William CurtinBrown University
Ductile versus brittle fracture in refractory High Entropy Alloys: What can the atoms tell us?
The brittle-ductile transition in refractory body-centered-cubic (bcc) metals and alloys has been an unresolved theoretical topic for many years. With the emergence of multi-component near-random bcc “high entropy alloys (HEAs)” that exhibit impressive high-temperature strength, the Achilles heel of brittle fracture at room temperature is among the most pressing issues to understand and resolve. Microscopy of fracture in the bcc elements Nb, Mo, and W suggests that dislocation emission from the crack tip is a critical phenomenon that enables crack blunting and prevents cleavage failure. The BDT is thus proposed to be associated an intrinsic brittle(cleavage)-ductile(emission) process at a sharp crack, which is then intrinsically atomistic. Here, the intrinsic brittle/ductile response is analyzed within linear elastic fracture mechanics to identify the relevant material properties and fracture orientations in bcc systems. Material properties are then computed using first-principles or atomistic potentials and a criterion for ductility is derived [1]. That criterion is then used to assess a wide range of HEAs with some success. Alternative criteria and concepts are also discussed and compared. The role of alloy disorder is analyzed and found to promote ductility, but a surprising reason. Incorporating the ductility criterion into an alloy-design process [3] identifies a promising family of Hf-Mo-Nb-Ti HEAs with high strength, high temperature strength, and possibly sufficient ductility. Nonetheless, we also report on HEAs that show a typical ductile failure mode but have very modest tensile ductility, highlighting the need to go beyond BDT criteria in the development of suitable high-performance bcc HEAs.
The brittle-ductile transition in refractory body-centered-cubic (bcc) metals and alloys has been an unresolved theoretical topic for many years. With the emergence of multi-component near-random bcc “high entropy alloys (HEAs)” that exhibit impressive high-temperature strength, the Achilles heel of brittle fracture at room temperature is among the most pressing issues to understand and resolve. Microscopy of fracture in the bcc elements Nb, Mo, and W suggests that dislocation emission from the crack tip is a critical phenomenon that enables crack blunting and prevents cleavage failure. The BDT is thus proposed to be associated an intrinsic brittle(cleavage)-ductile(emission) process at a sharp crack, which is then intrinsically atomistic. Here, the intrinsic brittle/ductile response is analyzed within linear elastic fracture mechanics to identify the relevant material properties and fracture orientations in bcc systems. Material properties are then computed using first-principles or atomistic potentials and a criterion for ductility is derived [1]. That criterion is then used to assess a wide range of HEAs with some success. Alternative criteria and concepts are also discussed and compared. The role of alloy disorder is analyzed and found to promote ductility, but a surprising reason. Incorporating the ductility criterion into an alloy-design process [3] identifies a promising family of Hf-Mo-Nb-Ti HEAs with high strength, high temperature strength, and possibly sufficient ductility. Nonetheless, we also report on HEAs that show a typical ductile failure mode but have very modest tensile ductility, highlighting the need to go beyond BDT criteria in the development of suitable high-performance bcc HEAs.
Véronique LazarusENSTA - Institut Polytechnique de Paris
Perturbative approaches to study the propagation of complex-shaped cracks
Poh Leong HienNational University of Singapore
The localizing gradient damage model for dynamic fracture
The conventional gradient enhancement has been widely used to resolve mesh sensitivity issues during strain softening. However, it may induce a spurious damage growth phenomenon. This motivates the development of the so-called localizing gradient enhancement where the nonlocal interaction decreases with damage in the free energy statement. The ensuing balance equation resembles that of the conventional gradient enhancement, albeit with a higher order flux term that vanishes with damage. The localizing gradient enhancement has been adopted for different damage and/or plasticity models in quasi-static conditions and has been shown to give localized damage profiles at failure. In this presentation, we focus on the use of the localizing gradient damage model for dynamic fracture. Particularly, we consider the incorporation of a micro-inertia term in the nonlocal balance equation and discuss on the influence of this additional term on the model predictions. To facilitate an ease of use of the model, a simple numerical implementation in the commercial software ABAQUS will also be presented, by adopting the built-in thermal-mechanical elements, and the results benchmarked against available experimental data in the literature.
The conventional gradient enhancement has been widely used to resolve mesh sensitivity issues during strain softening. However, it may induce a spurious damage growth phenomenon. This motivates the development of the so-called localizing gradient enhancement where the nonlocal interaction decreases with damage in the free energy statement. The ensuing balance equation resembles that of the conventional gradient enhancement, albeit with a higher order flux term that vanishes with damage. The localizing gradient enhancement has been adopted for different damage and/or plasticity models in quasi-static conditions and has been shown to give localized damage profiles at failure. In this presentation, we focus on the use of the localizing gradient damage model for dynamic fracture. Particularly, we consider the incorporation of a micro-inertia term in the nonlocal balance equation and discuss on the influence of this additional term on the model predictions. To facilitate an ease of use of the model, a simple numerical implementation in the commercial software ABAQUS will also be presented, by adopting the built-in thermal-mechanical elements, and the results benchmarked against available experimental data in the literature.
Jean-Jacques MarigoÉcole Polytechnique
On the modelling of the crack nucleation by the variational approach to fracture
It is well known that the nucleation of cracks is not possible with Griffith's theory of fracture essentially because in that theory the stresses are not bounded. Gradient damage models or more generally phase field models have been introduced to compensate for this lack. Their construction follows a variational approach which is based on clear physical principles, allows rigorous mathematical results and facilitates its numerical implementation. However, the most used models of this type like Ambrosio-Tortorelli' model leads to too simple strength criteria. Moreover the size of the yield stress surface depends on a parameter which tends to infinity when this parameter goes to zero. Therefore, those phase field models must be improved. In the talk, we will see as it is possible to construct phase field models such that the yield stress surface be as general as possible (with the unique restriction to be convex) and the size of which remains finite when the small regularizing parameter tends to zero. For that, it is not necessary to leave the comfortable variational approach and we will even show that the variational approach makes it possible to obtain a limit model which is entirely coherent. In particular the procedure will be developed for the construction of a model of fracture of an initially incompressible material which contains a fix limit for the spherical part of the stress tensor.
It is well known that the nucleation of cracks is not possible with Griffith's theory of fracture essentially because in that theory the stresses are not bounded. Gradient damage models or more generally phase field models have been introduced to compensate for this lack. Their construction follows a variational approach which is based on clear physical principles, allows rigorous mathematical results and facilitates its numerical implementation. However, the most used models of this type like Ambrosio-Tortorelli' model leads to too simple strength criteria. Moreover the size of the yield stress surface depends on a parameter which tends to infinity when this parameter goes to zero. Therefore, those phase field models must be improved. In the talk, we will see as it is possible to construct phase field models such that the yield stress surface be as general as possible (with the unique restriction to be convex) and the size of which remains finite when the small regularizing parameter tends to zero. For that, it is not necessary to leave the comfortable variational approach and we will even show that the variational approach makes it possible to obtain a limit model which is entirely coherent. In particular the procedure will be developed for the construction of a model of fracture of an initially incompressible material which contains a fix limit for the spherical part of the stress tensor.
Olivier AllixUniversité Paris-Saclay
Extension of quasi-static damage meso-modelling of composite laminates
to dynamic failure and erosion
Impact tests on structures are destructive, costly and difficult to analyze. This is particularly true for composite structures, whose properties and failure mechanisms are highly dependent on the chosen stacking architecture. As a result, virtual testing is of paramount importance for the design of composite structures subjected to impact ... but difficult.
Because of the practical importance of laminated composites, and thanks to fifty or more years of intensive research, the response to static failure is now well understood. At the meso level, this involves microcracking, fiber breakage, delamination and their interaction. Since the damage mechanisms typical of laminated composites with continuous long fibers are the same in both static and dynamic conditions, we can hope to extend the static meso-modeling of laminated composites to the dynamic.
Another aspect is that, in today's industrial environment, due to the lack of robustness of the local constitutive model, important numerical parameters such as mesh density are fixed in order to calibrate the model against a reference test. This process is tedious, and only allows the safe analysis of variations around well-controlled situations. The most widespread approach to overcoming the lack of consistency of the material model with regard to fracture is that of non-local spatial approaches, including phase-field approaches. In the case of composites, where numerous scales and mechanisms need to be addressed, these methods have yet to be developed and validated.
We therefore tried another possibility, that of regularization using a time-dependent model, which is quite natural in dynamics. It appears that using a usual rate-dependent model is not sufficient to circumvent all the problems associated with spurious damage localization in the dynamics. This is why we have proposed and developed the concept bounded rate damage model. A consequence of the model is that a minimum critical time is required to completely damage the material. The coupling between time and space seems to prevent parasitic localization, at least in our experience to date.
The presentation will cover these aspects, the basis for meso-modeling laminate damage and the limited damage rate model, as well as some applications and adaptations to dynamic delamination and damage, fracture and erosion of laminates subjected to high-speed impact.
Impact tests on structures are destructive, costly and difficult to analyze. This is particularly true for composite structures, whose properties and failure mechanisms are highly dependent on the chosen stacking architecture. As a result, virtual testing is of paramount importance for the design of composite structures subjected to impact ... but difficult.
Because of the practical importance of laminated composites, and thanks to fifty or more years of intensive research, the response to static failure is now well understood. At the meso level, this involves microcracking, fiber breakage, delamination and their interaction. Since the damage mechanisms typical of laminated composites with continuous long fibers are the same in both static and dynamic conditions, we can hope to extend the static meso-modeling of laminated composites to the dynamic.
Another aspect is that, in today's industrial environment, due to the lack of robustness of the local constitutive model, important numerical parameters such as mesh density are fixed in order to calibrate the model against a reference test. This process is tedious, and only allows the safe analysis of variations around well-controlled situations. The most widespread approach to overcoming the lack of consistency of the material model with regard to fracture is that of non-local spatial approaches, including phase-field approaches. In the case of composites, where numerous scales and mechanisms need to be addressed, these methods have yet to be developed and validated.
We therefore tried another possibility, that of regularization using a time-dependent model, which is quite natural in dynamics. It appears that using a usual rate-dependent model is not sufficient to circumvent all the problems associated with spurious damage localization in the dynamics. This is why we have proposed and developed the concept bounded rate damage model. A consequence of the model is that a minimum critical time is required to completely damage the material. The coupling between time and space seems to prevent parasitic localization, at least in our experience to date.
The presentation will cover these aspects, the basis for meso-modeling laminate damage and the limited damage rate model, as well as some applications and adaptations to dynamic delamination and damage, fracture and erosion of laminates subjected to high-speed impact.
