Papers by Harika Tankasala
International Journal of Fracture, Jul 11, 2017
The competition between crack penetration and crack kinking is addressed for a mode I macroscopic... more 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.
Acta Materialia, Oct 1, 2019
Additive manufacture and rapid prototyping are versatile methods for the generation of lattice ma... more Additive manufacture and rapid prototyping are versatile methods for the generation of lattice materials for applications in the creep regime. However, these techniques introduce defects that can degrade the macroscopic creep strength. In the present study, the uniaxial tensile response of two-dimensional PMMA lattices is measured in the visco-plastic regime: tests are performed at 100 • C which is slightly below the glass transition temperature T g of PMMA. Both as-manufactured defects (Plateau borders and strut thickness variation) and as-designed defects (missing cell walls, solid inclusions, and randomly perturbed joints) are introduced. The dispersion in macroscopic strength is measured for relative densities in the range of 0.07 to 0.19. It is observed that initial failure of the lattice is diffuse in nature: struts fail at a number of uncorrelated locations, followed by the development of a single macroscopic crack transverse to the loading direction. In contrast, the same PMMA lattice fails in a correlated, brittle manner at room temperature. An FE study is performed to gain insight into the diffuse failure mode and the role played by as-manufactured defects, including the dispersion in tensile strength of individual struts of the lattice. A high damage tolerance to as-designed defects is observed experimentally: there is negligible knock-down in strength due to the removal of cell walls or to the presence of solid inclusions. These findings aid the design and manufacture of damage tolerant lattices in the creep regime.
The in-plane elastic-plastic response of an incompressible, filled hexagonal honeycomb
Journal of The Mechanics and Physics of Solids, Oct 1, 2021
Abstract Exact solutions are derived for the small-strain, in-plane, elasto-plastic response of a... more Abstract Exact solutions are derived for the small-strain, in-plane, elasto-plastic response of a hexagonal honeycomb using slender beam theory; incompressibility of the honeycomb is enforced by filling its voids with an incompressible, inviscid fluid. The honeycomb has sides of equal length, but its inclined struts subtend an angle that can deviate from 120° with respect to the vertical side walls. The relative density is sufficiently small that the struts are slender and can be treated as Euler-Bernoulli beams. Exact solutions are obtained for the elastic moduli and macroscopic yield surface of the rigid, ideally plastic lattice under general in-plane loading: the solutions satisfy equilibrium, compatibility and the constitutive response of each elastic, ideally plastic beam. Prior to conducting an elastic analysis, and a rigid, ideally plastic analysis, initial insight is gained by exploring the vector space of inextensional collapse mechanisms of the pin-jointed, compressible version of the hexagonal truss. Two inextensional collapse mechanisms of the compressible honeycomb are identified from the null space of the kinematic matrix. The presence of an incompressible, inviscid fluid in the voids of the honeycomb locks-up one mechanism but the other mechanism survives and generates macroscopic shear strain. Consequently, the incompressible hexagonal honeycomb with rigid joints has a high shear compliance and a low shear strength, with values equal to that of the unfilled, compressible honeycomb. In contrast, macroscopic tensile straining of the incompressible honeycomb requires the stretching of bars in addition to bar-bending, and the tensile modulus and strength of the incompressible honeycomb are thereby elevated. Explicit analytical formulae are derived for the macroscopic tensile modulus and strength of the incompressible honeycomb.
International Journal of Fracture, Jul 5, 2018
The macroscopic tensile strength of a panel containing a centre-crack or a centre-hole is predict... more 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 predic-
International Journal of Solids and Structures, Apr 1, 2020
The degree to which the toughness of a lattice material can be enhanced by the suitable placement... more 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 (R-curve) to the cell wall strain hardening exponent and cell wall ductility is determined. Three concepts for enhancing the R-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.
Acta Materialia, Jun 1, 2019
Rapid prototyping is an emerging technology for the fast make of engineering components. A common... more Rapid prototyping is an emerging technology for the fast make of engineering components. A common technique is to laser cut a two-dimensional (2D) part from polymethyl methacrylate (PMMA) sheet. However, both manufacturing defects and design defects (such as stress raisers) exist in the part, and these degrade its strength. In the present study, a combination of experiment and finite element analysis is used to determine the sensitivity of the tensile strength of PMMA hexagonal lattices to both as-manufactured and as-designed defects. The as-manufactured defects include variations in strut thickness and in Plateau border radius. The knockdown in lattice tensile strength is measured for lattice relative density in the range of 0.07 to 0.19. A systematic finite element (FE) study is performed to assess the explicit role of each type of as-manufactured defect on the lattice strength. As-designed defects such as randomly perturbed joints, missing cells, and solid inclusions are introduced within a regular hexagonal lattice. The notion of a transition flaw size is used to quantify the sensitivity of lattice strength to defect size.
Journal of The Mechanics and Physics of Solids, Aug 1, 2020
An assessment is made of the J-integral test procedure for initial crack growth in an opencell al... more An assessment is made of the J-integral test procedure for initial crack growth in an opencell aluminium alloy foam by combining finite element (FE) simulations with experiment. It is found experimentally that a zone of randomly failed struts develops ahead of the primary crack tip, and is comparable in size to that of the plastic zone. Hence, a crack tip J-field is absent at the initiation of crack growth from the primary crack tip. This implies that the measured J IC value and the J versus crack extension ∆a curve cannot be treated as material properties despite the fact that the specimen size meets the usual criteria for J validity. The toughness tests were performed on a single-edge notched bend specimen, and crack extension was measured by the direct current potential drop method, by digital image correlation and by X-ray computed tomography. The crack growth resistance of the foam is associated with two distinct zones of plastic dissipation: (i) a bulk plastic zone emanating from the crack tip (containing a cluster of randomly failed struts), and (ii) a crack bridging zone behind the advancing crack tip. The applicability of a cohesive zone model to predict the fracture response is explored for the observed case of large scale bridging. To do so, FE simulations are performed by replacing the discrete lattice of the open-cell metallic foam by a compressible, elastic-plastic hardening solid while the fracture process zone in the foam is represented by a cohesive zone, as characterised by a tensile traction versus separation law. A detailed comparison of the cohesive zone model with experimental observations reveals that it is possible to capture the load versus displacement response but not the details of the fracture process zone using a single set of process zone parameters.
The in-plane elastic-plastic response of an incompressible, filled hexagonal honeycomb
Journal of the Mechanics and Physics of Solids, 2021
Abstract Exact solutions are derived for the small-strain, in-plane, elasto-plastic response of a... more Abstract Exact solutions are derived for the small-strain, in-plane, elasto-plastic response of a hexagonal honeycomb using slender beam theory; incompressibility of the honeycomb is enforced by filling its voids with an incompressible, inviscid fluid. The honeycomb has sides of equal length, but its inclined struts subtend an angle that can deviate from 120° with respect to the vertical side walls. The relative density is sufficiently small that the struts are slender and can be treated as Euler-Bernoulli beams. Exact solutions are obtained for the elastic moduli and macroscopic yield surface of the rigid, ideally plastic lattice under general in-plane loading: the solutions satisfy equilibrium, compatibility and the constitutive response of each elastic, ideally plastic beam. Prior to conducting an elastic analysis, and a rigid, ideally plastic analysis, initial insight is gained by exploring the vector space of inextensional collapse mechanisms of the pin-jointed, compressible version of the hexagonal truss. Two inextensional collapse mechanisms of the compressible honeycomb are identified from the null space of the kinematic matrix. The presence of an incompressible, inviscid fluid in the voids of the honeycomb locks-up one mechanism but the other mechanism survives and generates macroscopic shear strain. Consequently, the incompressible hexagonal honeycomb with rigid joints has a high shear compliance and a low shear strength, with values equal to that of the unfilled, compressible honeycomb. In contrast, macroscopic tensile straining of the incompressible honeycomb requires the stretching of bars in addition to bar-bending, and the tensile modulus and strength of the incompressible honeycomb are thereby elevated. Explicit analytical formulae are derived for the macroscopic tensile modulus and strength of the incompressible honeycomb.
Journal of the Mechanics and Physics of Solids, 2020
An assessment is made of the J-integral test procedure for initial crack growth in an opencell al... more An assessment is made of the J-integral test procedure for initial crack growth in an opencell aluminium alloy foam by combining finite element (FE) simulations with experiment. It is found experimentally that a zone of randomly failed struts develops ahead of the primary crack tip, and is comparable in size to that of the plastic zone. Hence, a crack tip J-field is absent at the initiation of crack growth from the primary crack tip. This implies that the measured J IC value and the J versus crack extension ∆a curve cannot be treated as material properties despite the fact that the specimen size meets the usual criteria for J validity. The toughness tests were performed on a single-edge notched bend specimen, and crack extension was measured by the direct current potential drop method, by digital image correlation and by X-ray computed tomography. The crack growth resistance of the foam is associated with two distinct zones of plastic dissipation: (i) a bulk plastic zone emanating from the crack tip (containing a cluster of randomly failed struts), and (ii) a crack bridging zone behind the advancing crack tip. The applicability of a cohesive zone model to predict the fracture response is explored for the observed case of large scale bridging. To do so, FE simulations are performed by replacing the discrete lattice of the open-cell metallic foam by a compressible, elastic-plastic hardening solid while the fracture process zone in the foam is represented by a cohesive zone, as characterised by a tensile traction versus separation law. A detailed comparison of the cohesive zone model with experimental observations reveals that it is possible to capture the load versus displacement response but not the details of the fracture process zone using a single set of process zone parameters.
International Journal of Solids and Structures, 2019
The degree to which the toughness of a lattice material can be enhanced by the suitable placement... more 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 cell walls are treated as truss elements, with each strut endowed with an axial tension versus elongation response, rather than treated as continuum. The axial response of each bar is based upon 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 are performed under smallscale yielding conditions, and the sensitivity of the crack growth resistance curve (R-curve) to the cell wall strain hardening exponent and cell wall ductility is determined. Three concepts for enhancing the R-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.
Acta Materialia, 2019
Additive manufacture and rapid prototyping are versatile methods for the generation of lattice ma... more Additive manufacture and rapid prototyping are versatile methods for the generation of lattice materials for applications in the creep regime. However, these techniques introduce defects that can degrade the macroscopic creep strength. In the present study, the uniaxial tensile response of two-dimensional PMMA lattices is measured in the visco-plastic regime: tests are performed at 100 • C which is slightly below the glass transition temperature T g of PMMA. Both as-manufactured defects (Plateau borders and strut thickness variation) and as-designed defects (missing cell walls, solid inclusions, and randomly perturbed joints) are introduced. The dispersion in macroscopic strength is measured for relative densities in the range of 0.07 to 0.19. It is observed that initial failure of the lattice is diffuse in nature: struts fail at a number of uncorrelated locations, followed by the development of a single macroscopic crack transverse to the loading direction. In contrast, the same PMMA lattice fails in a correlated, brittle manner at room temperature. An FE study is performed to gain insight into the diffuse failure mode and the role played by as-manufactured defects, including the dispersion in tensile strength of individual struts of the lattice. A high damage tolerance to as-designed defects is observed experimentally: there is negligible knock-down in strength due to the removal of cell walls or to the presence of solid inclusions. These findings aid the design and manufacture of damage tolerant lattices in the creep regime.
International Journal of Fracture, 2018
Acta Materialia, 2019
Rapid prototyping is an emerging technology for the fast make of engineering components. A common... more Rapid prototyping is an emerging technology for the fast make of engineering components. A common technique is to laser cut a two-dimensional (2D) part from polymethyl methacrylate (PMMA) sheet. However, both manufacturing defects and design defects (such as stress raisers) exist in the part, and these degrade its strength. In the present study, a combination of experiment and finite element analysis is used to determine the sensitivity of the tensile strength of PMMA hexagonal lattices to both as-manufactured and as-designed defects. The as-manufactured defects include variations in strut thickness and in Plateau border radius. The knockdown in lattice tensile strength is measured for lattice relative density in the range of 0.07 to 0.19. A systematic finite element (FE) study is performed to assess the explicit role of each type of as-manufactured defect on the lattice strength. As-designed defects such as randomly perturbed joints, missing cells, and solid inclusions are introduced within a regular hexagonal lattice. The notion of a transition flaw size is used to quantify the sensitivity of lattice strength to defect size.
International Journal of Mechanical Sciences, 2019
There is a practical need to elevate both the indentation strength and level of energy absorption... more There is a practical need to elevate both the indentation strength and level of energy absorption of engineering foams by the addition of a stiff and strong face sheet for applications such as packaging and crash mitigation. In this study, the enhancement in plane strain indentation resistance of a polyvinyl chloride (PVC) foam by the presence of a polycarbonate (PC) face sheet is determined by experiment, finite element analysis and by an analytical model. Plane strain indentation is by a flat-bottom punch or by a cylindrical roller, and the strain distribution within the PC face sheet and in the foam substrate are measured by digital image correlation. With increasing indent depth, the face sheet bends and stretches elastically and then plastically until face sheet or substrate fail. The generation of membrane tension in the face sheet plays a major role in supporting the indentation load when the indent depth exceeds the thickness of the face sheet, and leads to a strong hardening behaviour beyond the initial collapse load for indentation. Finite element predictions of the full indentation response are based upon the measured tensile and compressive responses of the PVC foam and PC layer. An analytical model is developed by matching the stretching response of the PC face sheet to the indentation response of the underlying foam, with due consideration for load diffusion from membrane tension of the PC face sheet into the underlying foam substrate. The indentation model is calibrated by ancillary finite element simulations of the load diffusion problem, and they emphasise the role of a shear lag zone in dictating the large indentation resistance. The indentation response of the bi-layer is also compared with that of a sandwich beam in 3-point bending. Experiments, finite element simulations and an additional analytical model for indentation of the sandwich beam in 3-point bending reveal that strong hardening of the post-yield load versus displacement response is now absent, in contrast to that of the bi-layer. The lack of hardening in 3-point bending is traced to the relatively low value of plastic bending moment of the beam section.
International Journal of Fracture, 2017
The competition between crack penetration and crack kinking is addressed for a mode I macroscopic... more 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.
Journal of the Mechanics and Physics of Solids, 2017
The finite strain, uniaxial tensile response of two-dimensional (2D) elastoplastic lattices is in... more The finite strain, uniaxial tensile response of two-dimensional (2D) elastoplastic lattices is investigated using finite element simulations and analytical models, taking into full account the macroscopic stiffening due to cell wall alignment. Four morphologies of 2D lattice are considered: triangular, Kagome, hexagonal, and diamond. The cell walls are treated as Timoshenko beams made from an elastoplastic solid with a strain hardening characteristic that resembles Ramberg-Osgood at low strains and exponential hardening at large strains. This description captures the response of metallic lattices at small strain and selected polymeric lattices at large strain. The use of beam theory is validated by additional continuum element simulations. The dependence of macroscopic ductility and tensile strength of each lattice is determined as a function of relative density, cell wall rupture strain and cell wall strainhardening. Two failure criteria are invoked: (i) maximum value of local tensile strain anywhere in the lattice attains a pre-defined failure strain, or (ii) maximum value of average tensile strain across any section of the lattice attains the failure strain. The sensitivity of macroscopic ductility and ultimate tensile strength to geometric imperfection is explored by considering: (i) random topologies in which the joints are randomly perturbed in position, and (ii) a finite crack formed by an array of broken cell walls. The notion of a transition flaw size for the lattices is validated by means of a notch sensitivity analysis, and the significance of crack-tip blunting by cell wall alignment is highlighted for the hexagonal honeycomb.
Journal of Applied Mechanics, 2015
The dependence of the fracture toughness of two-dimensional (2D) elastoplastic lattices upon rela... more The dependence of the fracture toughness of two-dimensional (2D) elastoplastic lattices upon relative density and ductility of cell wall material is obtained for four topologies: the triangular lattice, kagome lattice, diamond lattice, and the hexagonal lattice. Crack-tip fields are explored, including the plastic zone size and crack opening displacement. The cell walls are treated as beams, with a material response given by the Ramberg–Osgood law. There is choice in the criterion for crack advance, and two extremes are considered: (i) the maximum local tensile strain (LTS) anywhere in the lattice attains the failure strain or (ii) the average tensile strain (ATS) across the cell wall attains the failure strain (which can be identified with the necking strain). The dependence of macroscopic fracture toughness upon failure strain, strain hardening exponent, and relative density is obtained for each lattice, and scaling laws are derived. The role of imperfections in degrading the frac...
In the current study, we explore the regimes of two competing crack growth mechanisms in composit... more In the current study, we explore the regimes of two competing crack growth mechanisms in composites: self-similar crack extension as a result of fi ber tensile damage and 90 o kinking as a result of matrix shear damage. Through fi nite 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 suffi ciently long shear damage zones a panel with a sharp crack is much tougher and stronger than the one with a circular hole.
Deutsche Forschungsgemeinschaft (DFG) Grant recipients WA Bosbach and A Presas DFG grant BO 4961/3-1
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Papers by Harika Tankasala