Undamaged Material Research Articles

Experimental determination of residual flexural strength and critical buckling load of impact-damaged glass/epoxy laminates

The main objective of this research is to find experimentally the effect of impact damage on the flexural strength of glassfiber/epoxy laminated composite materials at two different test conditions. The other objective is to determine the criticalbuckling load of laminated composite material after impact loading. Thus, the loss of flexural and buckling performances ofthe damaged material has been established by comparison with the undamaged material. Initially, angle-ply laminatedcomposite plates with rectangular shaped have been subjected to impact load at different energy levels by using a dropweighttesting machine and impact damage has been created. To find the residual flexural strength, four-point bending testshave been carried out. Four-point bending specimens have been cut from the damaged area of the middle of the laminatedplates and have been positioned in two different ways according to the face subjected to the impact. For buckling tests, aunidirectional compression load has been applied to the impacted specimens with the size of 100 mm x150 mm. Accordingto the four-point bending test results, the flexural strengths of the specimens subjected to impact at 10 J and 30 J havedecreased approximately 25 and 42%, respectively. Similarly, the reductions in critical buckling loads of specimenssubjected to impact at 10 J and 40 J are approximately 16 and 32%, respectively. Consequently, the impact load significantlyreduces the flexural and buckling performances of laminated glass/epoxy composites. Furthermore, the positioning of thefour-point bending test specimen affects the flexural strength.

A 3D non-orthogonal plastic damage model for concrete

A plastic damage model with the non-orthogonal flow rule is developed, which is consisted of the damage part driven by plastic strain and the plastic part based on effective stress. In the damage characterization, the degeneration law of elastic stiffness is described by the damage variable in the form of exponential function. In the plastic characterization, the evolution for plastic strain increment (PSI) is characterized from the magnitude and direction perspective. The direction of PSI is obtained directly by the fractional gradient of yield surface and the need for the construction of plastic potential function is bypassed. The magnitude of PSI is calculated based on the effective hardening function and the yield function, where the effective hardening function corresponding to the undamaged material is derived by both the normal hardening/softening function corresponding to the damaged material and the damage variable. The Next Increment Corrects Error (NICE) algorithm integrating the computational accuracy and efficiency is used for the numerical implementation of model. The ability of model to capture the complex mechanical behavior of concrete is assessed by the monotonous and cyclic test data from the literature.

Nanoindentation Study of the Effect of Low-Temperature Ion Irradiation on the Hardness of a Ferritic–Martensitic EK-181 Steel

The hardness of a ferritic–martensitic steel EK-181 after ion irradiation to a maximum damaging dose of ~50 dpa in the temperature range 250–400°C is investigated. Nanoindentation is used to measure the mechanical properties. The hardnesses of the layer damaged by ions and that of the undamaged bulk material are found. At temperatures below 300°C, softening at a dose below 10 dpa and hardening at high doses of ~50 dpa are observed. Hardening is detected over the entire dose range at 400°C. The maximum hardness of the sample irradiated to ~50 dpa at 400°C is 1.7 GPa.

Electrical treeing: A phase-field model

Electrical treeing is a commonly observed phenomenon associated with dielectric breakdown in solid dielectrics. In this work, a phase-field model is developed to study the initiation and propagation of electrical trees in two different geometries: a parallel capacitor and a cylindrical capacitor. The model utilizes a continuous field of damage variable to distinguish the localized damaged regions from the undamaged bulk material. Factors that affect electrical tree morphology, including discharge speed and damage mobility, are studied. Electrical treeing tends to exhibit a fractal shape with more branches at a relatively high discharge speed relative to the rate of damage. Furthermore, the effect of fillers on electrical treeing is also studied. Numerical results suggest that fillers of lower permittivity, higher breakdown energy or lower damage mobility will promote fractal treeing and thus resist catastrophic breakdown.

Energy Analysis of the Deformation and Failure Process of Sandstone and Damage Constitutive Model

The damage theory was introduced to clarify and simulate the strain softening property of rocks. On the basis of the theory, an energy method was utilized to portray the rock mechanical properties from microscopic perspective. Firstly, from the perspective of rock microstructure, damage variable (expressed as D) was redefined by dividing the rock into three portions: undamaged materials, damaged materials and micro-defects, and an impact factor was introduced as the connection between the damaged material and the micro-defects. Meanwhile, the method for determining the impact factor was presented. Secondly, the damage variable was redefined in light of energy dissipation, then damage evolution analysis was conducted based on triaxial tests. An improved rock damage constitutive model was further obtained in another expression to reflect the energy change law. Subsequently, the relationship between D and the deformation and failure process of rocks was analyzed on account of the damage evolution equation formularized by fitting to a logistic function, which can measure the influence of energy dissipation on the propagation of micro-defects. By comparing between experimental results and theoretical results of illustrative examples, the effectiveness of the improved model was validated, and the its application was also discussed.

A Theory of Undamageable Graphene

It is the aim of this work to develop and extend the theory of undamageable materials to graphene. An undamageable material is a material where the value of the damage variable remains zero throughout the deformation process. It is anticipated that the constitutive equations for undamageable graphene can be modeled with differential equations for the case of graphene. The equations are solved for three cases: n = 1, n = 2, and the general case of n. It is hoped that undamageable graphene can be achieved in the laboratory in the near future when the manufacturing technology advances so as to produce such materials.

Advances in the mechanics of undamageable materials: General three-dimensional formulation

The theory of undamageable materials is extended to general states of deformation and damage. Undamageable materials are hypothetical materials that do not undergo any damage processes under the action of forces within the framework of continuum damage mechanics. In these types of materials, the damage variable remains zero throughout the deformation process. The authors developed previously the theory of undamageable materials for the one-dimensional case using scalars. In this work, the general three-dimensional formulation is presented using tensors. In this regard, a system of nonlinear partial differential equations governing the mechanics of undamageable materials is obtained. An attempt is made to solve the governing system using one single simplifying assumption. It is hope that the theoretical formulation presented in this work will open the way for future development of these types of new materials in practical applications.

Recommendations and interpretations for the tortuosity and pore-connectivity parameter in undamaged cement-based materials

Unsaturated transport properties, such as hydraulic conductivity (K), are commonly viewed as durability parameters for cement-based materials. Measuring K experimentally, however, is challenging due to high-pressure requirements at low degrees of saturation. For this reason, analytical expressions for hydraulic conductivity are often employed. Possibly the most widely used model for this purpose is the van Genuchten–Mualem equation. Usage of this equation requires employment of the tortuosity and pore-connectivity parameter I, which has significant implications on K. Often, a default value of is used, which leads to misrepresentation of K at low degrees of saturation. Recent works have identified the need for proper estimation of I, however uncertainty as to the realistic range for I still exists. In this paper, recommended ranges of I are developed for undamaged cement-based materials using analytical modeling based on physical realizations of unsaturated hydraulic properties. Interpretations of I are then presented based on the derived models.

Effects of Imperfections in Heat Straightening Repair of Steel Beam Bridges

A 40 ft. long two-span continuous steel bridge with two composite beams was constructed in the laboratory and subjected to damage followed by heat straightening repair. A36 steel section (W30 × 90) was used for the main girders (beams). Four spans (specimens) of the test bridge were statically damaged at each midspan using a hydraulic actuator, and subsequently repaired by applying Vee heats and restraining forces in the damaged region. Restraining force magnitude (corresponding to 0.4 Mp: 6.2 kips and 0.6 Mp: 9.5 kips), maximum heating temperature (800°F, 1200°F, and 1400°F), and the number of multiple damage-repair cycles (one and three cycles) were considered as the test parameters. The steel material properties were measured by taking samples from the repaired areas, and compared with undamaged steel material properties. Samples taken from specimens subjected to overheating (up to 1400°F) had similar structural properties and fracture toughness values as those taken from specimens subjected to normal heating (up to 1200°F). Specimens repaired with overstraining (0.6 Mp) combined with underheating (up to 800°F) required the largest number of heating cycles to fully repair the same damage. The fracture toughness of samples taken from specimens subjected to multiple (three times) damage-repair cycles was lower (decreased to about 84%) than the fracture toughness of samples taken from specimens subjected to only one damage-repair cycle. Therefore, multiple heat straightening repairs of a damaged beam should be performed with caution. With reference to serviceability performance for AASHTO HL-93 live load, the midspan deflections of beam specimens subjected to damage and heat straightening repair were comparable to those of undamaged beam specimens.

Autonomous high‐temperature healing of surface cracks in Al2O3 containing Ti2AlC particles

AbstractIn this work, the oxidation‐induced crack healing of Al2O3 containing 20 vol.% of Ti2AlC MAX phase inclusions as healing particles was studied. The oxidation kinetics of the Ti2AlC particles having an average diameter of about 10 μm was studied via thermogravimetry and/or differential thermal analysis. Surface cracks of about 80 μm long and 0.5 μm wide were introduced into the composite by Vickers indentation. After annealing in air at high temperatures, the cracks were filled with stable oxides of Ti and Al as a result of the decomposition of the Ti2AlC particles. Crack healing was studied at 800, 900, and 1000°C for 0.25, 1, 4, and 16 hours, and the strength recovery was measured by 4‐point bending. Upon indentation, the bending strength of the samples dropped by about 50% from 402 ± 35 to 229 ± 14 MPa. This bending strength increased to about 90% of the undamaged material after annealing at 1000°C for just 15 minutes, while full strength was recovered after annealing for 1 hour. As the healing temperature was reduced to 900 and 800°C, the time required for full‐strength recovery increased to 4 and 16 hours, respectively. The initial bending strength and the fracture toughness of the composite material were found to be about 19% lower and 20% higher than monolithic alumina, respectively, making this material an attractive substitute for monolithic alumina used in high‐temperature applications.

Environmentally enhanced creep crack growth by grain boundary cavitation under cyclic loading

Plane strain finite element calculations of mode I crack growth are carried out under small scale creep conditions with an imposed stress intensity factor that is a prescribed cyclic function of time. The finite deformation analyses are based on a constitutive relation that couples creep deformation and damage due to grain boundary cavitation including a simple model of the embrittling effect of solute (oxygen) diffusion along grain boundaries. Isothermal analyses are carried out for two sets of material and grain boundary parameters: (i) parameter values representative of HASTELLOY® X; and (ii) parameter values representative of P91. A stronger detrimental effect of environmentally assisted grain boundary embrittlement is found for HASTELLOY® X than for P91. For a fixed imposed stress intensity factor range the detrimental effect is found to increase with increased hold time for HASTALLOY® X. The variation of the predicted cyclic crack growth rate with imposed stress intensity factor range is found to be in good quantitative agreement with experimental results in the literature for both HASTELLOY® X and P91. Paris law behavior, i.e. the cyclic crack growth rate depending on the imposed stress intensity factor range raised to a power, emerges naturally in the calculations. Parametric studies show that the cyclic crack growth rate and the Paris law exponent are more sensitive to variations in the grain boundary diffusivity, the solute diffusivity and a parameter characterizing the environmental embrittling effect than to parameters characterizing the creep response of the undamaged material. Also, an explicit analytical expression is found that gives a very good fit to the computed dependence of the cyclic crack growth rate on the solute diffusivity.

Numerical Study and Experimental Validation of Effect of Varying Fiber Crack Density on Stiffness Reduction in CFRP Composites

Representative volume element (RVE) has commonly been used to predict the stiffness of undamaged composite materials using finite element analysis (FEA). However, never has been an independently measured true microstructural damage quantity used in FEA to predict composite stiffness. Hence, in this work, measured fiber crack density in unidirectional fiber composite (generated using controlled fatigue loading) was used to predict reduction in stiffness using a RVE. It was found that the stiffness changes with change in depth of the volume element along the fiber direction and asymptotically reaches a constant value beyond a critical length called representative depth. It was argued that this representative depth should be more than the minimum of two characteristic length scales, twice of ineffective length and average length of broken fibers. Effective stiffness obtained from FEA of the optimum-sized RVE was in excellent agreement with the experimental results for given microstructural damage state.

Simulating damage onset and evolution in fully bio-resorbable composite under three-point bending.

This paper presents a strain-based damage model to predict the stress-strain relationship and investigate the damage onset and evolution of the fibre and matrix of a fully bio-resorbable phosphate glass fibre reinforced composite under three-point bending. The flexural properties of the composite are crucial, particularly when it is employed as implant for long bone fracture. In the model, the 3D case of the strain and stress was used and the response of the undamaged material was assumed to be linearly elastic. The onset of damage was indicated by two damage variables for the fibre and matrix, respectively. The damage evolution law was based on the damage variable and the facture energy of the fibre and matrix, individually. A finite element (FE) model was created to implement the constitutive model and conduct numerical tests. An auto-adaptive algorithm is integrated in the FE model to improve the convergence. The FE model was capable of predicting the flexural modulus with around 3% relative error, and the flexural strength within 2% relative error in comparison with the experimental data. The numerical indices showed that the top surface of the sample was the most vulnerable under three-point bending. It was also found that the damage initiated in the fibre, was the primary driver for composite failure under three-point bending.

Phase-Field Modelling of Fracture in Viscoelastic Solids

The phase-field modeling has emerged as an extremely powerful numerical method to simulate crack propagation with significant success. The crack is herein modeled by a field variable that distinguishes between fully broken and undamaged material. In the proposed phase-field model for crack propagation in viscoelastic solids, a model with a fracture threshold similar to gradient damage theories is developed which can distinguish between fracture behavior in compression and tension. A viscoelastic material model in the framework of finite deformations is used for rubber-like material response. The full model is implemented in the framework of the FE program FEAP and allows both a monolithic and a staggered scheme for the numerical solution. Within FEAP a parameter study is realized. Finally, a summary of the results is presented and an outlook for improvements of the modeling for fracture in viscoelastic solids is given.

Level set topology optimization considering damage

This paper provides a level set based topology optimization approach to design structures exhibiting resistance to damage. The geometry of the structures is represented by the level set method. The design domains are discretized by the extended finite element method allowing for fixed non conforming meshes. The mechanical model represents quasi-brittle materials. Undamaged material behavior is assumed linear elastic while a loss of stiffness is introduced through a non-local damage model. Small strains are assumed. The sensitivities are evaluated by an analytical derivation of the discretized governing equations of the system and considering the adjoint approach. As the damage process is irreversible, the structural responses are path-dependent and this dependency is accounted for in the sensitivity analysis. The optimization problems are solved by mathematical programming algorithms, in particular using the GCMMA scheme. The proposed approach is illustrated with two dimensional examples that highlight the influence of degradation on the optimized designs.

Deuterium retention and thermal conductivity in ion-beam displacement-damaged tungsten

Retention of plasma-implanted D is studied in W targets damaged by a Cu ion beam at up to 0.2dpa with sample temperatures between 300K and 1200K. At a D plasma ion fluence of 1024/m2 on samples damaged to 0.2dpa at 300K, the retained D retention inventory is 4.6 ×1020D/m2, about ∼5.5 times higher than in undamaged samples. The retained inventory drops to 9 ×1019D/m2 for samples damaged to 0.2dpa at 1000K, consistent with onset of vacancy annealing at a rate sufficient to overcome the elevated rate of ion beam damage; at a damage temperature of 1200K retention is nearly equal to values seen in undamaged materials. A nano-scale technique provides thermal conductivity measurements from the Cu-ion beam displacement damaged region. We find the thermal conductivity of W damaged to 0.2dpa at room temperature drops from the un-irradiated value of 182 ± 3.3W/mK to 53 ± 8W/mK.

Effect of helium irradiation on deuterium permeation behavior in tungsten

In this study, we measured deuterium (D) gas-driven permeation through tungsten (W) foils that had been pre-damaged by helium ions (He+). The goal of this work was to determine how ion-induced damage affects hydrogen isotope permeation. At 873 K, the D permeability for W irradiated by 3.0 keV He+ was approximately one order of magnitude lower than that for un-damaged W. This difference diminished with increasing temperature. Even after heating to 1173 K, the permeability returned to less than half of the value measured for un-damaged W. We propose that this is due to nucleation of He bubbles near the surface which potentially serve as a barrier to diffusion deeper into the bulk. Exposure at higher temperatures shows that the D permeability and diffusion coefficients return to levels observed for undamaged material. It is possible that these effects are linked to annealing of defects introduced by ion damage, and whether the defects are stabilized by the presence of trapped He.

Embedding-Free Method for Preparation of Cross-Sections of Organic Materials for Micro Chemical Analysis Using Gas Cluster Ion Beam Sputtering.

We present a novel in situ mask method for the preparation of cross-sections of organic materials such as polymer multilayer films suitable for chemical imaging of buried interfaces. We demonstrate this method on a model buried interface system consisting of a piece of Scotch tape adhered to a PET substrate and a protective film used in consumer packaging. A high dose of gallium from a focused ion beam (FIB) was used to produce a damaged overlayer on the surface of the organic sample. The damaged layer has a significantly slower sputter rate compared to the native undamaged organic material. Therefore, during gas cluster ion beam (GCIB) depth profiling experiments the damaged layer functions as a mask, protecting the sample beneath and producing a cross-section at the edge of the mask. The FIB itself cannot be used directly to prepare the cross-section since the organic materials are easily damaged. A four step workflow is described including a final cleaning procedure to remove redeposited material from the cross-section. The workflow is completed in a few hours for samples up to 100 μm thickness. The method does not require sample embedding and is suited to automated analysis, which can be important benefits for industrial analysis where a variety of samples are analyzed routinely.

A multiscale model of distributed fracture and permeability in solids in all-round compression

We present a microstructural model of permeability in fractured solids, where the fractures are described in terms of recursive families of parallel, equidistant cohesive faults. Faults originate upon the attainment of tensile or shear strength in the undamaged material. Secondary faults may form in a hierarchical organization, creating a complex network of connected fractures that modify the permeability of the solid. The undamaged solid may possess initial porosity and permeability. The particular geometry of the superposed micro-faults lends itself to an explicit analytical quantification of the porosity and permeability of the damaged material. The model is the finite kinematics version of a recently proposed porous material model, applied with success to the simulation of laboratory tests and excavation problems [De Bellis, M. L., Della Vecchia, G., Ortiz, M., Pandolfi, A., 2016. A linearized porous brittle damage material model with distributed frictional-cohesive faults. Engineering Geology 215, 10–24. Cited By 0. 10.1016/j.enggeo.2016.10.010]. The extension adds over and above the linearized kinematics version for problems characterized by large deformations localized in narrow zones, while the remainder of the solid undergoes small deformations, as typically observed in soil and rock mechanics problems. The approach is particularly appealing as a means of modeling a wide scope of engineering problems, ranging from the prevention of water or gas outburst into underground mines, to the prediction of the integrity of reservoirs for CO2 sequestration or hazardous waste storage, to hydraulic fracturing processes.

Stress estimates for particle damage in Fe-TiB 2 metal matrix composites from experimental data and simulation

Abstract Experimental data regarding microstructural damage evolution in Fe-TiB 2 composites are examined in order to estimating the fracture stress of the TiB 2 particles in relation to their size distribution. At first, an a priori “on/off” particle breaking mode is introduced in a numerical modelling based on nonlinear homogenization methods, considering a three (matrix plus undamaged and damaged particles) phase assemblage. Specific effects on the stress estimates in the particles and on the damage evolution, due to particle shape and elasticity anisotropy, to matrix grain size and hardening, as well as to the loading mode, are examined in comparison with a reference estimate from a fully isotropic description of the undamaged material. The firstly assumed “on/off” brutal particle damage description is shown to overestimate both the damage-induced porosity in the material and the matrix hardening. Both are then adjusted with the available data using a much lower and gradual decrease of the TiB 2 particle stiffness from the undamaged state. From these adjustments, estimates of the size-related particle fracture stresses are obtained. Particle fracturing occurs with limited and gradual stiffness loss of the composite, consistently with a quite good bonding of the TiB 2 particles with the surrounding ferrite matrix.