Strength and toughness of planar ductile lattices

The effective medium properties of planar lattices made from ductile cell-wall materials are obtained analytically for four periodic topologies: the regular triangular honeycomb, the Kagome lattice, the +45o square lattice, and the regular hexagonal honeycomb, by assuming a power–law relation between cell-wall plastic stress and strain. The strength of the ductile lattice is estimated as the remote macroscopic stress leading to critical strain in a cell-wall anywhere in the lattice. The functional form of fracture toughness in terms of relative density and cell-wall material properties is estimated analytically and determined numerically from the asymptotic problem of a long crack. The results show that the stiffness, onset-of-yield stress, and strength are significantly higher for stretching topologies, i.e., the triangular honeycomb and the Kagome lattice. The presence of an elastic deformation zone surrounding the crack-tip plastic zone in Kagome and the formation of a shear lag zone along the lattice principal directions in square lattice lead to a toughness that is much higher than anticipated. Analytical and numerical predictions are also made for the transition crack length below which the lattice discreteness and crack-tip plasticity ensure un-notched strength, and beyond which the lattice is prone to brittle fracture. The dependence of transition length on the ratio of cell-wall material failure strain to yield strain is shown to be beneficial for increasing the damage tolerance of otherwise flaw-sensitive triangular and hexagonal honeycombs

Toughening due to shear kinking in composites

In the current study, we explore the regimes of two competing crack growth mechanisms in composites: self-similar crack extension as a result of fiber tensile damage and 90o kinking as a result of matrix shear damage. Through finite element calculations it is shown that the two damage zones extend and simultaneously shield each other under loading. Such cooperative shielding of the damage zones has a synergistic effect on the composite strength and toughness. Although the constitutive properties of the damage zones determine their relative extent, it is assumed that the preferred direction of crack extension is governed by the maximum energy release rate. The numerical values of strength and toughness against tensile/shear damage are obtained for a range of relative strength and ductility of the two damage zones. It is shown that a relatively weak and ductile shear zone is capable of increasing the macroscopic toughness by orders of magnitude. Conditions for the existence of such shear bands are stated for a range of orthotropy and a comparison is made on the toughness, strength, and preferred crack growth directions. The numerical model is then applied for an elliptical hole to examine the other extreme form of stress concentration. The extent of the shear damage is enhanced by the severity of orthotropy and initial stress concentration. As a result of this, for sufficiently long shear damage zones a panel with a sharp crack is much tougher and stronger than the one with a circular hole

Crack kinking at the tip of a mode I crack in an orthotropic solid.

The competition between crack penetration and crack kinking is addressed for a mode I macroscopic crack in an orthotropic elastic solid. Cohesive zones of finite peak strength and finite toughness are placed directly ahead of and orthogonal to the plane of the parent crack. The cohesive zone ahead of the crack tip is tensile in nature and leads to crack penetration, whereas the inclined zones slide without opening under a combined shear and normal traction, and give crack kinking. Thereby, the competition between continued crack growth by penetration ahead of the crack tip versus kinking is determined as a function of the relative strength and relative toughness of the cohesive zones. This competition is plotted in the form of a failure mechanism map, with the role of material orthotropy emphasized. Synergistic toughening is observed, whereby the parent crack tip is shielded by the activation of both the tensile and shear (kinking) cohesive zones, and the macroscopic toughness is elevated. The study is used to assess the degree to which various classes of composite have the tendency to undergo kinking

The crack growth resistance of an elastoplastic lattice

The degree to which the toughness of a lattice material can be enhanced by the suitable placement of multiple phases is explored. To achieve this, the resistance to mode I and mode II crack growth in a two-dimensional (2D), elastoplastic, triangulated lattice is investigated using finite element (FE) simulations. The fully triangulated lattice is idealised as a pin-jointed truss, and each strut has an axial force versus elongation (or shortening) characteristic based on the uniaxial tensile response of an elastoplastic solid with power-law hardening. When the tensile force in the strut attains a critical value, a linear softening law is adopted for the force versus elongation response of the strut to simulate its failure. FE simulations of crack growth in the 2D lattice are performed under small-scale yielding conditions, and the sensitivity of the crack growth resistance curve (curve) to the cell wall strain hardening exponent and cell wall ductility is determined. Three concepts for enhancing the curve of a triangulated lattice are explored: (i) a brittle lattice reinforced by long ductile fibres transverse to the cracking plane, (ii) a bilattice such that a small scale brittle lattice is reinforced by a large scale ductile lattice, and (iii) a 2D version of an interpenetrating lattice wherein a large-scale ductile lattice is bonded at its joints to an underlying small-scale brittle lattice.The authors gratefully acknowledge the financial support from the European Research Council (ERC) in the form of an advanced grant, MULTILAT, GA669764

Crack kinking at the tip of a mode I crack in an orthotropic solid

The competition between crack penetration and crack kinking is addressed for a mode I macroscopic crack in an orthotropic elastic solid. Cohesive zones of finite peak strength and finite toughness are placed directly ahead of and orthogonal to the plane of the parent crack. The cohesive zone ahead of the crack tip is tensile in nature and leads to crack penetration, whereas the inclined zones slide without opening under a combined shear and normal traction, and give crack kinking. Thereby, the competition between continued crack growth by penetration ahead of the crack tip versus kinking is determined as a function of the relative strength and relative toughness of the cohesive zones. This competition is plotted in the form of a failure mechanism map, with the role of material orthotropy emphasized. Synergistic toughening is observed, whereby the parent crack tip is shielded by the activation of both the tensile and shear (kinking) cohesive zones, and the macroscopic toughness is elevated. The study is used to assess the degree to which various classes of composite have the tendency to undergo kinking

2019 Proceedings of the 2nd International Conference on Trauma Surgery Technology in Giessen (Germany)

It is now for a second time that we can invite researchers to come to Giessen for an international exchange of the latest research and a discussion of ideas. This year again, the Deutsche Forschungsgemeinschaft (DFG) is sponsoring the event. The main topic for 2019 is 'Vibration in antibacterial and oncological therapy'. Many effects of mechanical vibration on tissue have been discovered so far. Clinical applications relying on vibration exist for a variety of conditions. The intracellular processes, however, are still largely not understood. And reproducibility remains a matter of potential for improvement. DFG funds for the 3rd conference in 2020 have already been approved for a focus on multifunctional trauma surgery implants.Deutsche Forschungsgemeischaft (DFG), German

Notch sensitivity of orthotropic solids: interaction of tensile and shear damage zones.

The macroscopic tensile strength of a panel containing a centre-crack or a centre-hole is predicted, assuming the simultaneous activation of multiple cohesive zones. The panel is made from an orthotropic elastic solid, and the stress raiser has both a tensile cohesive zone ahead of its tip, and shear cohesive zones in an orthogonal direction in order to represent two simultaneous damage mechanisms. These cohesive zones allow for two modes of fracture: (i) crack extension by penetration, and (ii) splitting in an orthogonal direction. The sensitivity of macroscopic tensile strength and failure mode to the degree of orthotropy is explored. The role of notch acuity and notch size are assessed by comparing the response of the pre-crack to that of the circular hole. This study reveals the role of the relative strength and relative toughness of competing damage modes in dictating the macroscopic strength of a notched panel made from an orthotropic elastic solid. Universal failure mechanism maps are constructed for the pre-crack and hole for a wide range of material orthotropies. The maps are useful for predicting whether failure is by penetration or kinking. Case studies are developed to compare the predictions with observations taken from the literature for selected orthotropic solids. It is found that synergistic strengthening occurs: when failure is by crack penetration ahead of the stress raiser, the presence of shear plastic zones leads to an enhancement of macroscopic strength. In contrast, when failure is by crack kinking, the presence of a tensile plastic zone ahead of the stress raiser has only a mild effect upon the macroscopic strength