Nicola Bonora

A nonlinear CDM model for ductile failure

Abstract Continuum Damage Mechanics (CDM) has bee proved to be a powerful tool in all those problems where it is difficult to use classical fracture mechanics concepts as a result of the following effects: effects of large-scale yielding plasticity (for instance, ductile rupture due to large deformations, geometry dependence of the J -resistance curve), three-dimensional effects, effects of multiple sites damage such as short cracks, multiple cracking in composites, and so on. In this paper, a new nonlinear CDM plasticity damage model is proposed. The model was developed on the experimental observations that the growth of microvoids results in a nonlinear damage accumulation with plastic deformation. Three basic possible damage evolution trends are identified and taken into account by a single damage model. The model proposed was applied successfully to seven different materials that clearly exhibit the three different damage evolution trends. The effects of triaxial state of stress on material damage parameters, such as the material strain to failure, are also discussed. Material damage constants and the procedure for their identification are presented.

Modeling ductile damage under fully reversed cycling

Abstract Damage mechanics has shown a great potential in predicting ductile material failure and, therefore, can be used to develop reliable tools for the design of components undergoing plastic deformation. In spite of the importance of cycling loading in components design, there are few examples of application of damage mechanics to fully reversed cycling. In this paper, the damage model proposed by Bonora [Eng. Fract. Mech. 58 (1997) 11] has been reformulated in order to account for compressive loading by introducing a new internal variable associated to damage. The model has been implemented into commercial finite element codes (MSC/MARC, ABAQUS). It was used to predict single element performance under cycling loading and damage accumulation in a round notched tensile bar. Some preliminary results are also discussed.

Low cycle fatigue life estimation for ductile metals using a nonlinear continuum damage mechanics model

Abstract Continuum damage mechanics is an effective approach to model ductile failure. The same concepts can be extended to the low cycle fatigue damage process, where plasticity is still the key mechanism for crack initiation. In addition, in low cycle fatigue a relevant part of life is spent by the material to initiate a macroscopic crack that leads to complete failure. In this paper, the nonlinear damage model, initially proposed by Bonora, N. (1997) A non-linear CDM model for ductile fracture Engineering Fracture Mechanics (in press), is extended to the case of cyclic loading. Three possible formulations are proposed and discussed that take into account in different ways the accumulation of damage, plastic strain and the material cyclic properties change. Fully coupled life model was used to predict low cycle fatigue life in AI 2024 T3 alloy and HY80 low carbon steel. Comparison with a large fatigue experimental data set is also presented.

The Pathogenesis of Retinal Damage in Blunt Eye Trauma: Finite Element Modeling

PURPOSE To test the hypothesis that blunt trauma shockwave propagation may cause macular and peripheral retinal lesions, regardless of the presence of vitreous. The study was prompted by the observation of macular hole after an inadvertent BB shot in a previously vitrectomized eye. METHODS The computational model was generated from generic eye geometry. Numeric simulations were performed with explicit finite element code. Simple constitutive modeling for soft tissues was used, and model parameters were calibrated on available experimental data by means of a reverse-engineering approach. Pressure, strain, and strain rates were calculated in vitreous- and aqueous-filled eyes. The paired t-test was used for statistical analysis with a 0.05 significance level. RESULTS Pressure at the retinal surface ranged between -1 and +1.8 MPa at the macula. Vitreous-filled eyes showed significantly lower pressures at the macula during the compression phase (P < 0.0001) and at the vitreous base during the rebound phase (P = 0.04). Multiaxial strain reached 20% and 25% at the macula and vitreous base, whereas the strain rate reached 40,000 and 50,000 seconds(-1), respectively. Both strain and strain rates at the macula, vitreous base, and equator reached lower values in the vitreous- compared with the aqueous-filled eyes (P < 0.001). Calculated pressures, strain, and strain rate levels were several orders of magnitude higher than the retina tensile strength and load-carrying capability reported in the literature. CONCLUSIONS Vitreous traction may not be responsible for blunt trauma-associated retinal lesions and can actually damp shockwaves significantly. Negative pressures associated with multiaxial strain and high strain rates can tear and detach the retina. Differential retinal elasticity may explain the higher tendency toward tearing the macula and vitreous base.

Identification and measurement of ductile damage parameters

Abstract The possibility of extending fracture mechanics concepts and design criteria to ductile failure is an issue that has attracted the attention of many researchers. Many models that address this are available nowadays. For these, two kinds of approach are widely used: the porosity-based model proposed by Gurson and the continuum damage mechanics (CDM) approach. Any new user that has to deal with these models for the first time is often hindered by the difficulty of finding in the literature, or measuring, the material parameters necessary. In addition, the use of these models, which are often available already built into commercial finite element codes, requires great experience and attention in order to avoid the danger of ‘numerical traps and tricks’. Here, constitutive models based on the plasticity criterion for porous media given by Gurson, and the CDM framework proposed by Lemaitre are reviewed, giving attention to identification procedures for the damage parameters.

Identification of the parameters of a non-linear continuum damage mechanics model for ductile failure in metals

Damage modelling in ductile metal has received a lot of attention in the last thirty years. Since 1969, many models have been proposed in the literature even though, in most of the cases, the experimental aspects related to the damage parameter evaluation have often been neglected. In this work the procedure to evaluate the damage parameters, for the continuum damage mechanics based model proposed by Bonora, is presented. Here, the ductile damage is experimentally measured in terms of progressive elastic modulus reduction as a function of strain measured in an hourglass-shaped specimen loaded in tension. The proposed technique, which is based on performing multiple, partial unloading, is reliable and relatively simple to implement. Additional tensile testing, performed with a round notch tensile bar, provides critical data that can be used to identify unequivocally the full damage parameter set and to assure their geometry transferability. The procedure presented here has been applied to identify the damage parameters for 20MnMoNi55 steel.

On the Effect of Triaxial State of Stress on Ductility Using Nonlinear CDM Model

Ductility takes into account the material capability to plastically deform. This parameter is not only modified by temperature but it is strongly affected by the stress triaxiality that, in the case of positive hydrostatic stress, reduces the material strain to failure. Due to the importance of this parameter in engineering design many attempts to predict the evolution of ductility with stress triaxiality have been done. Here, a nonlinear continuum damage model, as proposed by the author, is used to obtain the evolution of material ductility with stress triaxiality. The expression found relates the strain to failure in multi-axial state of stress regime only to the uniaxial strain to failure, to the damage strain threshold, to the material Poissons ratio, and, of course, to stress triaxiality. The proposed model was successfully verified comparing the predicted evolution of material ductility with the experimental data relative to several metals. The procedure for the damage parameters identification is also discussed in details.

Constitutive modeling for ductile metals behavior incorporating strain rate, temperature and damage mechanics

One the most serious limitation to an extensive use of computational techniques in simulating and predicting structures and components behavior under dynamic loading is given by the inadequacy of constitutive models to fairly represent failure process. In this paper a new constitutive model for ductile metals has been developed using the innovative solid state equation proposed by Milella (1998) and the non-linear damage model proposed by Bonora (1997). These two models are physically based and require a very limited number of constants that can be experimentally identified according to the procedures given by the authors. The implementation of the model in commercial finite element code is simple and cost effective with respect to similar nucleation and growth (NAG) models with the additional feature that hydrostatic pressure effect on ductile damage is correctly taken into account.

Primary blast injury to the eye and orbit: finite element modeling

PURPOSE Primary blast injury (PBI) mostly affects air-filled organs, although it is sporadically reported in fluid-filled organs, including the eye. The purpose of the present paper is to explain orbit blast injury mechanisms through finite element modeling (FEM). METHODS FEM meshes of the eye, orbit, and skull were generated. Pressure, strain, and strain rates were calculated at the cornea, vitreous base, equator, macula, and orbit apex for pressures known to cause tympanic rupture, lung damage, and 50% chance of mortality. RESULTS Pressures within the orbit ranged between +0.25 and -1.4 MegaPascal (MPa) for tympanic rupture, +3 and -1 MPa for lung damage, and +20 and -6 MPa for 50% mortality. Higher trinitrotoluene (TNT) quantity and closer explosion caused significantly higher pressures, and the impact angle significantly influenced pressure at all locations. Pressure waves reflected and amplified to create steady waves resonating within the orbit. Strain reached 20% along multiple axes, and strain rates exceeded 30,000 s(-1) at all locations even for the smallest amount of TNT. CONCLUSIONS The orbits pyramidlike shape with bony walls and the mechanical impedance mismatch between fluidlike content and anterior air-tissue interface determine pressure wave reflection and amplification. The resulting steady wave resonates within the orbit and can explain both macular holes and optic nerve damage after ocular PBI.

Microdamage effects on the overall response of long fibre/metal-matrix composites

Abstract Metal-matrix composites represent a new generation of material in which the mechanical properties of metals and the effectiveness of composite structure are matched together. Experimental work performed on SiC long fibre/Ti composites revealed that two distinct slopes can be identified on the overall stress/strain curve before the appearance of hardening effects. A microscopical investigation provided evidence of distributed fibre debonding after the application of load. Further consideration on the nature of the contact zone between fibre and matrix revealed that the interface is a very weak zone, in which the material properties are degraded by the action between SiC and reactive Ti matrix. The adhesion between fibre and matrix is mainly due to the gripping effect of the matrix, resulting from cooling after material manufacture. To develop a micromechanical model able to predict the overall response of a simple unidirectional laminate, a finite element investigation was carried out on the matrix zone surrounding a fibre. The existence of a periodic fibre array was assumed and a unit cell chosen as representative of the average behaviour of the array. The stress/strain field at the interface was evaluated, including the forming process of the material in the analysis. Numerical results were compared with experimental data. Damage computation was performed using a continuum damage mechanics formulation, to evaluate the interaction between the matrix plastic damage and the interface damage phenomena in the unit cell.