Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “STRAIN ENERGY”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 163 records · Page 9

Towards a damage tolerance philosophy for composite materials and structures

A damage-threshold/fail-safe approach is proposed to ensure that composite structures are both sufficiently durable for economy of operation, as well as adequately fail-safe or damage tolerant for flight safety. Matrix cracks are assumed to exist throughout the off-axis plies. Delamination onset is predicted using a strain energy release rate characterization. Delamination growth is accounted for in one of three ways: either analytically, using delamination growth laws in conjunction with strain energy release rate analyses incorporating delamination resistance curves; experimentally, using measured stiffness loss; or conservatively, assuming delamination onset corresponds to catastrophic delamination growth. Fail-safety is assessed by accounting for the accumulation of delaminations through the thickness. A tension fatigue life prediction for composite laminates is presented as a case study to illustrate how this approach may be implemented. Suggestions are made for applying the damage-threshold/fail-safe approach to compression fatigue, tension/compression fatigue, and compression strength following low velocity impact.

Obrien, T. Kevin↗

Towards a damage tolerance philosophy for composite materials and structures

A damage-threshold/fail-safe approach is proposed to ensure that composite structures are both sufficiently durable for economy of operation, as well as adequately fail-safe or damage tolerant for flight safety. Matrix cracks are assumed to exist throughout the off-axis plies. Delamination onset is predicted using a strain energy release rate characterization. Delamination growth is accounted for in one of three ways: either analytically, using delamination growth laws in conjunction with strain energy release rate analyses incorporating delamination resistance curves; experimentally, using measured stiffness loss; or conservatively, assuming delamination onset corresponds to catastrophic delamination growth. Fail-safety is assessed by accounting for the accumulation of delaminations through the thickness. A tension fatigue life prediction for composite laminates is presented as a case study to illustrate how this approach may be implemented. Suggestions are made for applying the damage-threshold/fail-safe approach to compression fatigue, tension/compression fatigue, and compression strength following low velocity impact.

O'Brien, T. Kevin↗

Enhancement of Nanostructured Ferritic Alloy 14YWT Properties via Heat Treatment for Post-Consolidation Processing

The nanostructured ferritic alloy 14YWT is a promising candidate for in-core use in generation IV nuclear reactors, due to a dense dispersion of insoluble, ultrafine-scale Y-Ti-O nano-oxides, which provide a high degree of irradiation tolerance and thermal stability. This work investigates the effects of heat treatment on the workability of 14YWT, along with the effect of processing history on abnormal grain structures and radial microstructural uniformity. In this study, a 14YWT rod consolidated at 850 °C was heat treated in argon at 1100 °C, 1150 °C, 1200 °C, or 1250 °C for 1 or 8 hours and changes in mechanical properties and microstructure were examined using microhardness and electron backscattered diffraction (EBSD). Two distinct types of large abnormal grains were observed, each with unique processing origins, including one with high and the other with low strain energy. Consolidation via direct extrusion resulted in radial microstructural gradients, where the center of the rod was softer with larger grain sizes and lower strain energies. These gradients persisted and intensified throughout heat treatment. Based upon this work, the recommended heat treatment for increased workability with minimal microstructural change is 1150 °C for 1 hours.

36 MATERIALS SCIENCE↗

Anisotropic strength behavior of single-crystal TATB

High-rate strength behavior plays an important role in the shock initiation of high explosives, with plastic deformation serving to localize heat into hot spots and as a mechanochemical means to enhance reactivity. Recent simulations predict that detonation-like shocks produce highly reactive nanoscale shear bands in the layered crystalline explosive TATB (1,3,5-triamino-2,4,6-trinitrobenzene), but the thresholds leading to this response are poorly understood. We utilize molecular dynamics to simulate the high-rate compressive stress–strain response of TATB, with a focus on understanding flow behavior. Here, the dependence of strength on pressure and loading axis (crystal orientation) is explored. The deformation mechanisms fall broadly into two categories, with compression along crystal layers activating a buckling/twinning mode and compression normal to the layers producing nanoscale shear bands. Despite the complexity of the underlying mechanisms, the crystal exhibits relatively straightforward stress–strain curves. Most of the crystal orientations studied show rapid strain softening following the onset of yielding, which settles to a steady flow state. Trajectories are analyzed using five metrics for local states and structural order, but most of these metrics yield similar distributions for these deformation mechanisms. On the other hand, a recently proposed measure of intramolecular strain energy is found to most cleanly distinguish between these mechanisms, while also providing a plausible connection with mechanochemically accelerated decomposition kinetics. Localization of intramolecular strain energy is found to depend strongly on crystal orientation and pressure.

36 MATERIALS SCIENCE↗

Comparison of full 3-D, thin-film 3-D, and thin-film plate analyses of a postbuckled embedded delamination

Local buckling can cause large interlaminar stresses along the delamination front, which can lead to delamination growth. This paper examines several methods of calculating strain-energy release rates, which are often used to predict delamination growth. The thin-film plate analysis, which was least expensive, calculated the total strain-energy release rate G(T) quite accurately. However, the stress field along the delamination front is highly mixed-mode and has no fixed ratio of G(I) to G(II). Since plate analysis can only calculate G(T), it would not be useful for accurate predictions of delamination growth if mode mix is important.

Whitcomb, John D.↗

Crack Development in Cross-Ply Laminates Under Uniaxial Tension

This study addresses matrix-dominated failures in carbon fiber/polymer matrix composite laminates in a cross-ply lay-up. The events of interest are interlaminar fracture in the form of transverse cracks in the 90' plies and longitudinal splitting in the 0 deg plies and interlaminar fracture in the form of 0/90 delamination. These events were observed using various nondestructive evaluation (NDE) techniques during static tensile tests. Acoustic emission (AE) x radiography, and edge view microscopy were the principal ones utilized in a real-time environment. A comparison of the NDE results with an analytical model based on the classical linear fracture mechanics concept of strain energy release rate as a criterion for crack growth was performed. The virtual crack closure theory was incorporated with a finite element model to generate strain energy release rate curves for the analytical case. Celion carbon fiber/polyimide matrix (G30-500/PMR-15) was the material tested with cross-ply lay-ups of (0(2)/90(6))s and (0(4)/90(4))s. The test specimens contained thermally induced cracks caused by the high-temperature processing. The analytical model was updated to compensate for the initial damage and to study further accumulation by taking into account the crack interactions. By correlating the experimental and analytical data, the critical energy release rates were found for the observable events of interest.

Gyekenyesi, Andrew L.↗

Tensor Basis Gaussian Process Models of Hyperelastic Materials

In this study, we develop Gaussian process regression (GPR) models of isotropic hyperelastic material behavior. First, we consider the direct approach of modeling the components of the Cauchy stress tensor as a function of the components of the Finger stretch tensor in a Gaussian process. We then consider an improvement on this approach that embeds rotational invariance of the stress-stretch constitutive relation in the GPR representation. This approach requires fewer training examples and achieves higher accuracy while maintaining invariance to rotations exactly. Finally, we consider an approach that recovers the strain-energy density function and derives the stress tensor from this potential. Although the error of this model for predicting the stress tensor is higher, the strain-energy density is recovered with high accuracy from limited training data. The approaches presented here are examples of physics-informed machine learning. They go beyond purely data-driven approaches by embedding the physical system constraints directly into the Gaussian process representation of materials models.

36 MATERIALS SCIENCE↗

Mixed-mode cyclic debonding of adhesively bonded composite joints

A combined experimental-analytical investigation to characterize the cyclic failure mechanism of a simple composite-to-composite bonded joint is conducted. The cracked lap shear (CLS) specimens of graphite/epoxy adherend bonded with EC-3445 adhesive are tested under combined mode 1 and 2 loading. In all specimens tested, fatigue failure occurs in the form of cyclic debonding. The cyclic debond growth rates are measured. The finite element analysis is employed to compute the mode 1, mode 2, and total strain energy release rates (i.e., GI, GII, and GT). A wide range of mixed-mode loading, i.e., GI/GII ranging from 0.03 to 0.38, is obtained. The total strain energy release rate, G sub T, appeared to be the driving parameter for cyclic debonding in the tested composite bonded system.

Rezaizadeh, M. A.↗

Thickness and orientational design for a maximum stiff membrane

Recent results from sensitivity analysis for strain energy with anisotropic elasticity are applied to thickness and orientational design of laminated membranes. Primarily, the first order gradients of the total elastic energy are used in an optimality criteria based method. This traditional method is shown to give slow convergence with respect to design parameters, although the convergence of strain energy is very good. To get a deeper insight into this rather general characteristic, second order derivatives are included and it is shown how they can be obtained by first order sensitivity analysis. Examples of only thickness design, only orientational design, and combined thickness--orientational design are presented.

Pedersen, Pauli↗

Adaptive finite element analysis based on p-convergence

The results of numerical experiments are presented in which a posteriori estimators of error in strain energy were examined on the basis of a typical problem in linear elastic fracture mechanics. Two estimators were found to give close upper and lower bounds for the strain energy error. The potential significance of this is that the same estimators may provide a suitable basis for adaptive redistribution of the degrees of freedom in finite element models.

Szabo, B. A.↗

On the use of the T-criterion in fracture mechanics

The applicability of the maximum dilatational strain energy density criterion, T-criterion, as proposed by Theocaris and Andrianopoulos, is investigated for use in a crack propagation study. It is found that the T-criterion has to be modified to correctly determine the fracture load. A detailed comparison between the minimum strain energy density criterion, S-criterion, and the new modified T-criterion is given for generalized plane stress and plane strain conditions.

Yehia, N. A. B.↗

Finite element analysis of instability related delamination growth

Instability-related growth of through-width delaminations in laminated coupons was investigated analytically and experimentally. In the analytical effort, a geometrically nonlinear finite-element stress analysis was used, and the numerical results were compared with exact solutions. In addition, measured lateral deflections of postbuckled through-width delaminations were compared with predicted deflections. Lateral deflections, stress distributions, and strain energy release rates were calculated for various delamination lengths, delamination depths, and applied loads. Delamination growth rates observed for unidirectional graphite/epoxy bonded to aluminum were qualitatively correlated with calculated strain-energy release rates and it was found that the Mode I component of energy release dominates the growth process.

Whitcomb, J. D.↗

Load biaxiality and fracture - Synthesis and summary

The question of load biaxiality strongly affecting almost all of the characteristics of brittle fracture behavior of a cracked body is investigated. Results of research published piecemeal over the years by the authors have shown that the stress and displacement fields, the elastic strain energy density, and the maximum shear stress near the crack tip are all altered by loads applied parallel to the crack, as are the angle of initial crack extension, the strain energy of the entire body, the fracture load, and the rate of fatigue crack growth. A synthesis and summary of this research is presented showing the shortcomings inherent in both Griffith's global energy rate theory for crack instability and Irwin's local crack-tip stress intensity theory for fracture toughness. In both theories only the tensile load perpendicular to the crack influences fracture behavior of the body.

Eftis, J.↗

Delamination durability of composite materials for rotorcraft

Delamination is the most commonly observed failure mode in composite rotorcraft dynamic components. Although delamination may not cause immediate failure of the composite part, it often precipitates component repair or replacement, which inhibits fleet readiness, and results in increased life cycle costs. A fracture mechanics approach for analyzing, characterizing, and designing against delamination will be outlined. Examples of delamination problems will be illustrated where the strain energy release rate associated with delamination growth was found to be a useful generic parameter, independent of thickness, layup, and delamination source, for characterizing delamination failure. Several analysis techniques for calculating strain energy release rates for delamination from a variety of sources will be outlined. Current efforts to develop ASTM standard test methods for measuring interlaminar fracture toughness and developing delamination failure criteria will be reviewed. A technique for quantifying delamination durability due to cyclic loading will be presented. The use of this technique for predicting fatigue life of composite laminates and developing a fatigue design philosophy for composite structural components will be reviewed.

Obrien, T. Kevin↗

Resistance To Delamination In Composite Materials

Fracture-mechanics approach applied to delamination failures. Report presents fracture-mechanics approach to analyzing, characterizing, and designing against delamination. In study, examples of delamination problems illustrated wherein strain-energy-release rate associated with growth of delamination useful generic parameter, independent of thickness, layup, and source of delamination, for characterization of failure by delamination. Several techniques for calculation of strain-energy-release rates for delaminations from variety of sources outlined. Technique for quantification of durability due to cyclic loading presented.

Obrien, T. Kevin↗

Rate effects on delamiantion fracture toughness of a toughened graphite/epoxy

The objective of this study was to determine the effects of loading rate on interlaminar fracture toughness of T300/F-185 graphite/epoxy composite, having an elastomer-modified epoxy resin matrix. Mode I interlaminar fracture was investigated by means of uniform width and width-tapered double cantilever beam (DCB) specimens. Hinged tabs were used to insure unrestrained rotation at the free ends. Specimens were loaded at quasi-static deflection rates of up to 8.5 mm/s corresponding to crack extension rates of up to 21 mm/s. Crack extension was monitored by means of strain gages mounted on the surface of the specimen. Continuous records were obtained of load, deflection, and crack extension for determination of the strain energy release rate. The latter was calculated by means of the area method and beam analysis method, and expressed as a power law of the crack extension velocity. Results indicate that the strain energy release rate decreases with crack velocity by over 20 percent over three decades of crack velocity.

Daniel, Isaac M.↗

Finite element analysis of instability-related delamination growth

A parametric study of postbuckled through-width delaminations in laminated coupons was performed. A finite element analysis was developed to analyze the coupons as a combination of linear and geometrically nonlinear components. Because most of the coupon configuration studied behaves linearly, the mixed linear and nonlinear analysis greatly reduced computational costs. The analysis was verified by comparing numerical with exact solutions for simple hypothetical problems. In addition, measured lateral deflections of postbuckled through-width delaminations in laminated coupons were compared with predicted deflections. In the parametric study, stress distributions and strain-energy release rates were calculated for various delamination lengths, delamination depths, applied loads, and lateral deflections. Also, a small number of coupons with through-width delaminations were fatigue tested to obtain delamination growth data. Calculated strain-energy release rates were compared with the observed growth rates to determine the relative importance of the Mode 1 and Mode 2 components of energy release. Growth process was dominated by G sub I.

Whitcomb, J. D.↗

Delamination growth analysis in quasi-isotropic laminates under loads simulating low-velocity impact

A geometrically nonlinear finite-element analysis was developed to calculate the strain energy released by delamination plates during impact loading. Only the first mode of deformation, which is equivalent to static deflection, was treated. Both the impact loading and delamination in the plate were assumed to be axisymmetric. The strain energy release rate in peeling, G sub I, and shear sliding, G sub II, modes were calculated using the fracture mechanics crack closure technique. Energy release rates for various delamination sizes and locations and for various plate configurations and materials were compared. The analysis indicated that shear sliding (G sub II) was the primary mode of delamination growth. The analysis also indicated that the midplane (maximum transverse shear stress plane) delamination was more critical and would grow before any other delamination of the same size near the midplane region. The delamination growth rate was higher (neutrally stable) for a low toughness (brittle) matrix and slower (stable) for high toughness matrix. The energy release rate in the peeling mode, G sub I, for a near-surface delamination can be as high as 0.5G sub II and can contribute significantly to the delamination growth.

Shivakumar, K. N.↗