Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Stress strain relations”

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 199 records · Page 11
All sourcesNASA NTRSDOE OSTI
NASA NTRS2004

Investigation of Three-Dimensional Stress Fields and Slip Systems for FCC Single Crystal Superalloy Notched Specimens

Metals and their alloys, except for a few intermetallics, are inherently ductile, i.e. plastic deformation precedes fracture in these materials. Therefore, resistance to fracture is directly related to the development of the plastic zone at the crack tip. Recent studies indicate that the fracture toughness of single crystals depends on the crystallographic orientation of the notch as well as the loading direction. In general, the dependence of crack propagation resistance on crystallographic orientation arises from the anisotropy of (i) elastic constants, (ii) plastic deformation (or slip), and (iii) the weakest fracture planes (e.g. cleavage planes). Because of the triaxial stress state at the notch tips, many slip systems that otherwise would not be activated during uniaxial testing, become operational. The plastic zone formation in single crystals has been tackled theoretically by Rice and his co-workers and only limited experimental work has been conducted in this area. The study of the stresses and strains in the vicinity of a FCC single crystal notch tip is of relatively recent origin. We present experimental and numerical investigation of 3D stress fields and evolution of slip sector boundaries near notches in FCC single crystal tension test specimens, and demonstrate that a 3D linear elastic finite element model that includes the effect of material anisotropy is shown to predict active slip planes and sectors accurately. The slip sector boundaries are shown to have complex curved shapes with several slip systems active simultaneously near the notch. Results are presented for surface and mid-plane of the specimens. The results demonstrate that accounting for 3D elastic anisotropy is very important for accurate prediction of slip activation near FCC single crystal notches loaded in tension. Results from the study will help establish guidelines for fatigue damage near single crystal notches.

Arakere, Nagaraj K.↗
NASA NTRS1953

A study of elastic and plastic stress concentration factors due to notches and fillets in flat plates

Six large 24s-t3 aluminum-alloy-sheet specimens containing various notches or fillets were tested in tension to determine their stress concentration factors in both the elastic and plastic ranges. The elastic stress concentration factors were found to be slightly higher than those calculated by Neuber's method and those obtained photoelastically by Frocht. The results showed further that the stress concentration factor decreases as strains at the discontinuity enter the plastic range. A generalization of Stowell's relation for the plastic stress concentration factor at a circular hole in an infinite plate was applied to the specimen shapes tested and gave good agreement with test results.

Hardrath, Herbert F↗
NASA NTRS1996

The Role of Musculoskeletal Dynamics and Neuromuscular Control in Stress Development in Bone

The role of forces produced by the musculotendon units in the stress development of the long bones during gait has not been fully analyzed. It is well known that the musculotendons act as actuators producing the joint torques which drive the body. Although the joint torques required to perform certain motor tasks can be recovered through a kinematic analysis, it remains a difficult problem to determine the actual forces produced by each muscle that resulted in these torques. As a consequence, few studies have focused on the role of individual muscles in the development of stress in the bone. This study takes a control theoretic approach to the problem. A seven-link, eight degrees of freedom model of the body is controlled by various muscle groups on each leg to simulate gait. The simulations incorporate Hill-type models of muscles with activation and contraction dynamics controlled through neural inputs. This direct approach allows one to know the exact muscle forces exerted by each musculotendon throughout the gait cycle as well the joint torques and reaction forces at the ankle and knee. Stress and strain computed by finite element analysis on skeletal members will be related to these derived loading conditions. Thus the role of musculoskeletal dynamics and neuromuscular control in the stress development of the tibia during gait can be analyzed.

DeWoody, Yssa↗
NASA NTRS1993

On the development of constitutive relations for metallic powders

This article describes the development of elastic and plastic constitutive relations as functions of relative density for partially consolidated -100 mesh aluminum powder. First, measurements of yield stress as a function of stress state and relative density are described. Measurements of the plastic strain increments associated with yielding in unconstrained compression tests and elastic properties, both as functions of relative density, are also described. The experimental results are combined with the associated flow rule to show that the yield surface is asymmetric with respect to hydrostatic tension and compression. Second, it is shown that the yield stress results can be represented by a two-part (capped Drucker-Prager) yield surface. The consolidation yield surface moves along the hydrostatic stress axis during densification, while the shear yield surface approaches the Mises yield surface. For the Al powder used in the present investigation, superposition of shear stress on a hydrostatic stress state aids the densification process. However, the hydrostatic stress requirement was found to be reduced by only about 20 pct for relative densities below 0.98.

Watson, T. J.↗
NASA NTRS1988

Life prediction of thermomechanical fatigue using total strain version of strainrange partitioning (SRP): A proposal

A method is proposed (without experimental verification) for extending the total strain version of Strainrange Partitioning (TS-SRP) to predict the lives of thermomechanical fatigue (TMF) cycles. The principal feature of TS SRP is the determination of the time-temperature-waveshape dependent elastic strainrange versus life lines that are added subsequently to the classical inelastic strainrange versus life lines to form the total strainrange versus life relations. The procedure is based on a derived relation between failure and flow behavior. Failure behavior is represented by conventional SRP inelastic strainrange versus cyclic life relations, while flow behavior is captured in terms of the cyclic stress-strain response characteristics. Stress-strain response is calculated from simple equations developed from approximations to more complex cyclic constitutive models. For applications to TMF life prediction, a new testing technique, bithermal cycling, is proposed as a means for generating the inelastic strainrange versus life relations. Flow relations for use in predicting TMF lives would normally be obtained from approximations to complex thermomechanical constitutive models. Bithermal flow testing is also proposed as an alternative to thermomechanical flow testing at low strainranges where the hysteresis loop is difficult to analyze.

Saltsman, James F.↗
DOE OSTI2024

On the Onset of Plasticity: Determination of Strength and Ductility

The analysis of the work hardening variation with stress reveals insight to operative stress-strain mechanisms in material systems. The onset of plasticity can be assessed and related to ensuing plastic deformation up to the structural instability using one constitutive relationship that incorporates both behaviors of rapid work hardening (Stage 3) and the asymptotic leveling of stress (Stage 4). Results are presented for the mechanical behavior analysis of Ti-6Al-4V wherein the work hardening variation of Stages 3 and 4 are found to: be dependent through a constitutive relationship; be useful in a Hall-Petch formulation of yield strength; and provide the basis for a two point-slope fit method to model the experimental work hardening and stress-strain behavior.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Stressful crystal histories recorded around melt inclusions in volcanic quartz

Abstract Magma ascent and eruption are driven by a set of internally and externally generated stresses that act upon the magma. We present microstructural maps around melt inclusions in quartz crystals from six large rhyolitic eruptions using synchrotron Laue X-ray microdiffraction to quantify elastic residual strain and stress. We measure plastic strain using average diffraction peak width and lattice misorientation, highlighting dislocations and subgrain boundaries. Quartz crystals across studied magma systems preserve similar and relatively small magnitudes of elastic residual stress (mean 53–135 MPa, median 46–116 MPa) in comparison to the strength of quartz (~ 10 GPa). However, the distribution of strain in the lattice around inclusions varies between samples. We hypothesize that dislocation and twin systems may be established during compaction of crystal-rich magma, which affects the magnitude and distribution of preserved elastic strains. Given the lack of stress-free haloes around faceted inclusions, we conclude that most residual strain and stress was imparted after inclusion faceting. Fragmentation may be one of the final strain events that superimposes stresses of ~ 100 MPa across all studied crystals. Overall, volcanic quartz crystals preserve complex, overprinted deformation textures indicating that quartz crystals have prolonged deformation histories throughout storage, fragmentation, and eruption.

58 GEOSCIENCES↗
NASA NTRS1981

Creep crack-growth: A new path-independent T sub o and computational studies

Two path independent integral parameters which show some degree of promise as fracture criteria are the C* and delta T sub c integrals. The mathematical aspects of these parameters are reviewed. This is accomplished by deriving generalized vector forms of the parameters using conservation laws which are valid for arbitrary, three dimensional, cracked bodies with crack surface tractions (or applied displacements), body forces, inertial effects and large deformations. Two principal conclusions are that delta T sub c is a valid crack tip parameter during nonsteady as well as steady state creep and that delta T sub c has an energy rate interpretation whereas C* does not. An efficient, small displacement, infinitestimal strain, displacement based finite element model is developed for general elastic/plastic material behavior. For the numerical studies, this model is specialized to two dimensional plane stress and plane strain and to power law creep constitutive relations.

Stonesifer, R. B.↗
NASA NTRS1982

Creep crack-growth: A new path-independent integral (T sub c), and computational studies

The development of valid creep fracture criteria is considered. Two path-independent integral parameters which show some degree of promise are the C* and (Delta T)sub c integrals. The mathematical aspects of these parameters are reviewed by deriving generalized vector forms of the parameters using conservation laws which are valid for arbitrary, three dimensional, cracked bodies with crack surface tractions (or applied displacements), body forces, inertial effects, and large deformations. Two principal conclusions are that (Delta T)sub c has an energy rate interpretation whereas C* does not. The development and application of fracture criteria often involves the solution of boundary/initial value problems associated with deformation and stresses. The finite element method is used for this purpose. An efficient, small displacement, infinitesimal strain, displacement based finite element model is specialized to two dimensional plane stress and plane strain and to power law creep constitutive relations. A mesh shifting/remeshing procedure is used for simulating crack growth. The model is implemented with the quartz-point node technique and also with specially developed, conforming, crack-tip singularity elements which provide for the r to the n-(1+n) power strain singularity associated with the HRR crack-tip field. Comparisons are made with a variety of analytical solutions and alternate numerical solutions for a number of problems.

Stonesifer, R. B.↗
NASA NTRS1987

Calculation of thermomechanical fatigue life based on isothermal behavior

The isothermal and thermomechanical fatigue (TMF) crack initiation response of a hypothetical material was analyzed. Expected thermomechanical behavior was evaluated numerically based on simple, isothermal, cyclic stress-strain - time characteristics and on strainrange versus cyclic life relations that have been assigned to the material. The attempt was made to establish basic minimum requirements for the development of a physically accurate TMF life-prediction model. A worthy method must be able to deal with the simplest of conditions: that is, those for which thermal cycling, per se, introduces no damage mechanisms other than those found in isothermal behavior. Under these assumed conditions, the TMF life should be obtained uniquely from known isothermal behavior. The ramifications of making more complex assumptions will be dealt with in future studies. Although analyses are only in their early stages, considerable insight has been gained in understanding the characteristics of several existing high-temperature life-prediction methods. The present work indicates that the most viable damage parameter is based on the inelastic strainrange.

Halford, Gary R.↗
NASA NTRS1987

Calculation of thermomechanical fatigue life based on isothermal behavior

The isothermal and thermomechanical fatigue (TMF) crack initiation response of a hypothetical material was analyzed. Expected thermomechanical behavior was evaluated numerically based on simple, isothermal, cyclic stress-strain-time characteristics and on strainrange versus cyclic life relations that have been assigned to the material. The attempt was made to establish basic minimum requirements for the development of a physically accurate TMF life-prediction model. A worthy method must be able to deal with the simplest of conditions: that is, those for which thermal cycling, per se, introduces no damage mechanisms other than those found in isothermal behavior. Under these assumed conditions, the TMF life should be obtained uniquely from known isothermal behavior. The ramifications of making more complex assumptions will be dealt with in future studies. Although analyses are only in their early stages, considerable insight has been gained in understanding the characteristics of several existing high-temperature life-prediction methods. The present work indicates that the most viable damage parameter is based on the inelastic strainrange.

Halford, G. R.↗
NASA NTRS2003

Fully Nonlinear Modeling and Analysis of Precision Membranes

High precision membranes are used in many current space applications. This paper presents a fully nonlinear membrane theory with forward and inverse analyses of high precision membrane structures. The fully nonlinear membrane theory is derived from Jaumann strains and stresses, exact coordinate transformations, the concept of local relative displacements, and orthogonal virtual rotations. In this theory, energy and Newtonian formulations are fully correlated, and every structural term can be interpreted in terms of vectors. Fully nonlinear ordinary differential equations (ODES) governing the large static deformations of known axisymmetric membranes under known axisymmetric loading (i.e., forward problems) are presented as first-order ODES, and a method for obtaining numerically exact solutions using the multiple shooting procedure is shown. A method for obtaining the undeformed geometry of any axisymmetric membrane with a known inflated geometry and a known internal pressure (i.e., inverse problems) is also derived. Numerical results from forward analysis are verified using results in the literature, and results from inverse analysis are verified using known exact solutions and solutions from the forward analysis. Results show that the membrane theory and the proposed numerical methods for solving nonlinear forward and inverse membrane problems are accurate.

Pai, P. Frank↗
NASA NTRS1991

High strain rate properties of off-axis composite laminates, part 2

Unidirectional off-axis graphite/epoxy and graphite/S-glass/epoxy laminates were characterized in uniaxial tension at strain rates ranging from quasi-static to over 500 s(sup -1). Laminate ring specimens were loaded by internal pressure with the tensile stress at 22.5, 30, and 45 degrees relative to the fiber direction. Results were presented in the form of stress-strain curves to failure. Properties determined included moduli, Poisson's ratios, strength, and ultimate strain. In all three laminates of both materials the modulus and strength increase sharply with strain rate, reaching values roughly 100, 150, and 200 percent higher than corresponding static values for the 22.5(sub 8), 30(sub 8), and 45(sub 8) degree laminates, respectively. In the case of ultimate strain no definite trends could be established, but the maximum deviation from the average of any value for any strain rate was less than 18 percent.

Daniel, I. M.↗
DOE OSTI2020

Transient solute drag and strain aging of dislocations

The transient drag force exerted by mobile solutes on a moving dislocation is computed using continuum theory. These mobile solutes form so-called Cottrell atmospheres around dislocations during static and dynamic strain aging. We evaluate the evolution of the drag force exerted by the atmosphere under two velocity time-histories: impulsive acceleration to a chosen velocity and a constant acceleration rate. A particular focus is on the conditions under which the stationary limit assumed by theories of dynamic strain aging is obeyed. According to our results, two conditions—one on the dislocation velocity and one on the acceleration rate—must be satisfied for the stationary limit to hold. Using the Orowan relation and a line tension model, we obtain estimates for the temperature, stress, strain rate, and dislocation density regimes where the stationary limit is valid, and compare these results with experiments for a few material systems.

36 MATERIALS SCIENCE↗
NASA NTRS1984

Influence of soft inclusions on the strength of wrought materials

The three dimensional soft particles (such as sulfides, silicates and voids) present in most materials are modelled by circular voids in sheet metal. Relationships are sought between the shape and orientation of a hole after rolling and testing in tension. Then, the effect of hole shape and size on mechanical properties is considered experimentally. The presence of voids has a negligible influence on the ultimate tensile stress of ductile materials based on the unperforated area because plastic flow neutralizes the stress intensification present in the elastic region. However, the shape and orientation of the defects are found to play an important role relative to strain at fracture. In certain engineering applications the strain at fracture is more important than the stress at fracture and in this sense the presence of voids are considered to influence the strength of a ductile material.

Pai, D. M.↗
DOE OSTI2025

In-situ synchrotron X-ray study on microstructure and stress evolutions of electroplated copper upon self-annealing

Background: The self-annealing behavior of electroplated copper (Cu) at room temperature is gaining attention in the microelectronics industry due to its significant impact on reliability issues such as substrate warpage and electrical resistivity. Methods: In this study, in-situ analysis of the microstructure transition and stress relaxation of the electroplated copper upon self-annealing was conducted via synchrotron white X-ray nanodiffraction (beamline 21A, Taiwan Photon Source) and grazing-incidence X-ray diffraction (beamline 17B1, Taiwan Light Source). Significant Findings: Remarkable relaxations of deviatoric stress and absolute strain component along the [002] direction were closely related to the Cu grain growth and crystallographic reorientation at the early stage of selfannealing, and a complete stress/strain relaxation can be achieved with the cessation of microstructure transition. In conclusion, the in-situ synchrotron X-ray studies provided an insight into Cu self-annealing mechanism, offering valuable information for improving Cu interconnect reliability.

Cu Self-annealing↗
DOE OSTI2020

Temporal dynamics of the alignment of the turbulent stress and strain rate

We report that the flux of energy between scales in turbulence can be cast as the result of the interaction between a turbulent stress and a rate of strain. Efficient energy transfer requires that these two tensors be oriented properly relative to each other, but previous work has shown that the instantaneous alignment between them is poor. Here, we consider the temporal dynamics of this alignment in a direct numerical simulation of isotropic turbulence. We show that the orientation of the stress lags behind that of the strain rate, both at a single location and along trajectories. However, the timescale of the reorientation of the stress in these cases does not follow the expected dynamical scaling with length scale. To capture the proper dynamical scaling, we reformulate the energy flux between scales using the right Cauchy-Green strain tensor and the second Piola-Kirchhoff stress tensor. Our results highlight the key role played by the deformation of fluid elements in the physics of the energy cascade, and suggest that their irreversible deformation is a Lagrangian manifestation of the cascade's broken time-reversal symmetry.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗