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Computational models based on the finite element method and linear or nonlinear fracture mechanics are herein proposed to study the mechanical response of functionally designed cellular components. It is demonstrated that, via a suitable tailoring of the properties of interfaces present in the meso- and micro-structures, the tensile strength can be substantially increased as compared to that of a standard polycrystalline material. Moreover, numerical examples regarding the structural response of these components when subjected to loading conditions typical of cutting operations are provided. As a general trend, the occurrence of tortuous crack paths is highly favorable: stable crack propagation can be achieved in case of critical crack growth, whereas an increased fatigue life can be obtained for a sub-critical crack propagation.

_{max} = crack length corresponding to the component failure (m)

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_{IC} = material fracture toughness (MPa m^{1/2})

_{IC}^{int} = interface fracture toughness (MPa m^{1/2})

_{c} = critical load for brittle crack propagation (N)

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ν = Poisson’s ratio (-)

ψ = inclination of the cellular rods with respect to the horizontal axis (°)

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Hard materials subjected to extreme loading conditions, high temperatures and severe impacts, as in case of cutting tools, have been the subject of extensive research to improve their performance. For instance, reducing the grain size of the material micro-structure down to the nanoscale is a common way to increase hardness, strength and wear resistance [

Recently, the introduction of functionally designed micro-structures opened new possibilities. In 2001, Fang

Scheme of a functionally designed cellular microstructure (reprinted with permission from [

Clearly, the presence of several design parameters makes the connection between the microstructure properties and the final mechanical response hard to be quantified. In particular, the presence of interfaces over different scales (finite thickness interfaces separating the cells and the grain boundaries between the PCD grains) makes the material characterization particularly challenging. At present, there is a lack of information about the effect of interface properties over multiple scales on the overall structural response. Understanding this connection is of paramount importance in order to improve the mechanical properties by tailoring the interface characteristics. In this context, virtual testing using numerical methods taking into account the heterogeneous composition of the material is expected to be beneficial.

In the present study, interfaces are not considered as simple defects,

In this section, the role of the two-level micro-structure on the fracture mechanics response of honeycomb cellular materials is numerically investigated using the finite element method and nonlinear fracture mechanics. To this purpose, let us consider the cross-sections of the material micro-structure shown in

Cross-sections of polycrystalline diamond (PCD) cellular rods with thick cell boundaries ((

This material is an example of a

Hence, at both levels we have material interfaces that are expected to influence the mechanical response. Experiments [

(

The statistical variability of interface fracture properties may affect the crack path in case of intergranular crack propagation, especially inside the PCD rods. In this regards, the CZM in [

Note that the micro- and meso-structures are not physically similar if different constitutive laws are used at the two levels. As a practical example, we consider interfaces at the second level to be tougher than those of the first level. In particular,

Shapes of the CZMs of the interfaces between the rods (level 2 or meso-structure).

Simulating virtual tensile tests on a representative volume element (RVE) of the material by imposing a monotonic horizontal displacement to the finite element nodes on the vertical sides of the RVE, the homogenized response can be computationally determined. The RVE is selected as to isolate the smallest repetitive part of the meso-structure.

Dimensionless tensile strength

The peak stress of the homogenized stress-strain curves,

The results in

Here, a multi-material component is considered, where an external layer made of PCD cells is bonded to a hard metal substrate (see

Sketch of a PCD bit used in cutting tools (reprinted with permission from [_{c} and different possible failure modes ranging from micro- to macro-chipping are sketched.

When subjected to repeated loadings, as during cutting operations, different failure modes may occur. In case of a horizontal load concentrated at the tool tip, _{c}, micro-, meso- and macro-chipping can take place, depending on the initiation point of a crack on the vertical side in tension, see

To investigate the effect of the rods on the crack pattern and on the stability of crack propagation, a FE model of the PCD layer with a cellular meso-structure is proposed. A rod diameter _{IC}(PCD) = 10.5 MPa m^{1/2}, _{IC}(WC-Co) = 30.0 MPa m^{1/2} and _{IC}(int) = 20 MPa m^{1/2}, see also [

Specific crack propagation criteria have to be considered for simulating interface fracture in the framework of linear elastic fracture mechanics. Among the criteria generally used, a distinction has to be made between local and global ones. Local fracture criteria can be used in those cases where the elastic fields lose self-similarity or the crack may not remain coplanar as it propagates [

(1) Crack propagation takes place along the interface or in one of the two adjacent materials along the direction

(2) Crack propagation begins as soon as one of the following conditions is satisfied:

where

On the other hand, global fracture criteria are essentially based on the energy balance and are generally applicable under the condition that the crack propagates along an interface or into a homogeneous medium [

otherwise it deflects into one of the neighborhood materials. This failure criterion was implemented in the FE Fracture ANalysis Code (FRANC2D) by Ingraffea and Wawrzynek [

(1) For each material region around a crack tip:

find the direction of the maximum tensile circumferential stress;

remesh to add a finite crack increment in this direction;

solve the resulting FE equations;

normalize the global change in strain energy with respect to the crack increment and compute the ratio with the critical energy release rate.

(2) For each interface around the crack tip:

extend the crack a finite distance along the interface;

solve the resulting FE equations;

use the relative opening and sliding at the crack tip to determine the load angle and the critical strain energy release rate;

normalize the change in strain energy with respect to the crack increment and find the ratio with the critical strain energy release rate.

(3) The direction of propagation is that with the largest associated ratio of the rate of energy release to the critical rate of energy release.

The use of the energy criterion is preferred here to the strength criterion. For crack propagation inside homogeneous materials, the global and the local criteria give predictions that fall in a very narrow band [

Considering the mechanical stress field due to a horizontal force acting at the tool tip, a magnification of the crack path is shown in

Fracture of a cutter with a cellular microstructure: scheme of the compact bit (

The critical load for crack propagation, _{c}, which corresponds to the critical condition for crack propagation at each step, is shown in _{max} is the final crack length when the crack meets the hard metal substrate and failure of the component takes place. At the beginning of the simulation, the crack propagates into a PCD road, and therefore there is no difference with respect to the propagation into a standard homogeneous material, at least in 2D simulations (see

These results are important as far as the issue of stability of crack propagation is concerned (see

For subcritical crack propagation, which may occur in case of repeated forces of magnitude lower than _{c}, similar numerical simulations can be performed and the Paris’ law can be applied to determine the crack growth rate, d

where

Dimensionless critical load for brittle crack propagation

Dimensionless crack length

The effects of rods’ inclination and interface fracture toughness are also investigated and the results are shown in

The effects of rods’ inclination and interface fracture toughness on fatigue life.

In this study it has been shown that functionally designed micro-structures can offer enhanced mechanical properties as compared to traditional polycrystalline materials. Tailoring of interface properties is the way to enhance the material tensile strength as compared to standard polycrystals. Moreover, interfaces can be used to enforce crack propagation along pre-defined paths, increasing the critical load for brittle crack propagation and the fatigue life of structural components. However, further investigations in this direction are necessary, especially regarding the effect of cellular structures on the properties related to contact mechanics,

The support of the Italian Ministry of Education, University and Research (MIUR), Ateneo Italo-Tedesco, and the Deutscher Akademischer Austausch Dienst (DAAD) to the Vigoni Project “3D modeling of crack propagation in polycrystalline materials” is gratefully acknowledged.