SEARCH · Engineering Papers

Results for “DEFORMATION”

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.

SourceResearch connectionFrom yearThrough year

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

At least 73 records · Page 4

All sources NASA NTRS DOE OSTI

NASA NTRS1973

Experimental stress analysis of large plastic deformations in a hollow sphere deformed by impact against a concrete block

An experimental plastic strain measurement system is presented for use on the surface of high velocity impact test models. The system was used on a hollow sphere tested in impact against a reinforced concrete block. True strains, deviatoric stresses, and true stresses were calculated from experimental measurements. The maximum strain measured in the model was small compared to the true failure strain obtained from static tensile tests of model material. This fact suggests that a much greater impact velocity would be required to cause failure of the model shell structure.

Morris, R. E.↗

NASA NTRS1993

Deformation mechanisms of NiAl cyclicly deformed near the brittle-to-ductile transition temperature

The intermetallic compound NiAl is one of many advanced materials which is being scrutinized for possible use in high temperature, structural applications. Stoichiometric NiAl has a high melting temperature, excellent oxidation resistance, and good thermal conductivity. Past research has concentrated on improving monotonic properties. The encouraging results obtained on binary and micro-alloyed NiAl over the past ten years have led to the broadening of NiAl experimental programs. The purpose of this research project was to determine the low cycle fatigue properties and dislocation mechanisms of stoichiometric NiAl at temperatures near the monotonic brittle-to-ductile transition. The fatigue properties were found to change only slightly in the temperature range of 600 to 700 K; a temperature range over which monotonic ductility and fracture strength increase markedly. The shape of the cyclic hardening curves coincided with the changes observed in the dislocation structures. The evolution of dislocation structures did not appear to change with temperature.

Cullers, Cheryl L.↗

NASA NTRS2004

Inverse FEM for Full-Field Reconstruction of Elastic Deformations in Shear Deformable Plates and Shells

The inverse problem of real-time reconstruction of full-field structural displacements is addressed through the application of a new variational formulation leading to versatile, robust and computationally efficient inverse shell finite element analysis. Utilizing surface strain measurements from strain sensors mounted on the load-carrying structural components, the methodology enables accurate computations of the three-dimensional displacement field. This high fidelity computational technology is essential for providing feedback to the actuation and control systems of the next generation of aerospace vehicles.

Tessler, Alexander↗

NASA NTRS1992

Contribution of vertebral deformities to chronic back pain and disability. The Study of Osteoporotic Fractures Research Group

Among 2992 white women aged 65-70 years recruited from population-based listings, we measured radiographic vertebral dimensions of T5-L4 and calculated ratios of heights: anterior/posterior, mid/posterior, and posterior/posterior of either adjacent vertebra. The degree of deformity for each vertebra was analyzed in terms of the number of standard deviations (SD) that ratio differed from the mean ratio calculated for the same vertebral level in this population. We correlated the severity of each woman's worst vertebral deformity with back pain, back disability in six activities of daily living, and height loss since age 25. Only 39.4% of the cohort had no vertebral deformity; 10.2% had a deformity greater than or equal to 4 SD. Vertebral deformities less than 4 SD below the mean were not associated with increased back pain, disability, or loss of height. In contrast, women whose deformity was greater than or equal to 4 SD had a 1.9 (95% CI, 1.5-2.4) times higher risk of moderate to severe back pain and a 2.6 (95% CI, 1.7-3.9) times higher risk of disability involving the back; they were also 2.5 (95% CI, 2.0-3.2) times more likely to have lost greater than or equal to 4 cm in height. All three types of vertebral deformity (wedge, end plate, and crush) were equally associated with these outcomes. Multiple deformities less than 4 SD did not increase the likelihood of these three outcomes, but multiple deformities greater than or equal to 4 SD tended to be associated with increased back pain, disability, and height loss. This large cross-sectional study suggests that vertebral deformities cause substantial pain, disability, or loss of height only if vertebral height ratios fall 4 SD below the normal mean. Much back pain could not be attributed to vertebral deformities, suggesting other causes.

Non-NASA Center↗

DOE OSTI2023

A High-Speed Rotational Diamond Anvil Cell for In Situ Analysis of Hierarchical Microstructural Evolution of Metallic Alloys during Extreme Shear Deformation

High speed shear deformation is ubiquitous in engineering applications, ranging from material processing methods such as friction stir processing/extrusion and in tribological contacts. However, analyzing the microstructural evolution of materials while they are undergoing high speed shear deformation have been a long-standing challenge. This led to predominant reliance on ex situ microscopy before and after shear deformation. But ex situ microscopy lacks the ability to analyze dynamic and transient hierarchical microstructural evolution mechanisms that could occur during shear deformation of materials. Therefore, to better understand the dynamic mechanisms of mass and energy transfer in materials under shear deformation, we developed a first of its kind high-speed rotational diamond anvil cell (HS-RDAC) for synchrotron-based in situ high-energy x-ray diffraction (XRD). We studied the time resolved lattice strain evolution, XRD peak broadening and changes in spatial variation of shear deformation induced alloying in pure metal and metal alloy sheets and powder mixture using the HS-RDAC. These in situ results were combined with detailed ex situ microstructural characterization before and after the shear deformation using transmission electron microscopy and atom probe tomography, which revealed the different stages of evolution of a shear deformation induced hierarchical nanostructure. Multiscale computational simulations including computational fluid dynamics, crystal plasticity, molecular dynamic simulation and density functional theory uncovered the mechanisms behind morphological changes, evolution of defect structures and changes in driving force for shear deformation induced intermixing. In conclusion, this in situ HS-RDAC capability, in combination with ex situ microstructural characterization and computational simulations, can provide new insights into the hierarchical microstructural evolution pathway during shear deformation.

36 MATERIALS SCIENCE↗

NASA NTRS1990

Innovative design of composite structures: Axisymmetric deformations of unsymmetrically laminated cylinders loaded in axial compression

The study focuses on the axisymmetric deformation response of unsymmetrically laminate cylinders loaded in axial compression by known loads. A geometrically nonlinear analysis is used. Though buckling is not studied, the deformations can be considered to be the prebuckling response. Attention is directed at three 16 layer laminates: a (90 sub 8/0 sub 8) sub T; a (0 sub 8/90 sub 8) sub T and a (0/90) sub 4s. The symmetric laminate is used as a basis for comparison, while the two unsymmetric laminates were chosen because they have equal but opposite bending-stretching effects. Particular attention is given to the influence of the thermally-induced preloading deformations that accompany the cool-down of any unsymmetric laminate from the consolidation temperature. Simple support and clamped boundary conditions are considered. It is concluded that: (1) The radial deformations of an unsymmetric laminate are significantly larger than the radial deformations of a symmetric laminate, although for both symmetric and unsymmetric laminates the large deformations are confined to a boundary layer near the ends of the cylinder; (2) For this nonlinear problem the length of the boundary layer is a function of the applied load; (3) The sign of the radial deformations near the supported end of the cylinder depends strongly on the sense (sign) of the laminate asymmetry; (4) For unsymmetric laminates, ignoring the thermally-induced preloading deformations that accompany cool-down results in load-induced deformations that are under predicted; and (5) The support conditions strongly influence the response but the influence of the sense of asymmetry and the influence of the thermally-induced preloading deformations are independent of the support conditions.

Hyer, M. W.↗

NASA NTRS1957

Study of the Micro-Nonuniformity of the Plastic Deformation of Steel

The plastic flow during deformation of real polycrystalline metals has specific characteristics which distinguish the plastic deformation of metals from the deformation of ordinary isotropic bodies. One of these characteristics is the marked micro-nonuniformity of the plastic deformation of metals. P.O. Pashkov demonstrated the presence of a considerable micro-nonuniformity of the plastic deformation of coarse-grained steel wit medium or low carbon content. Analogous results in the case of tension of coarse-grained aluminum were obtained by W. Boas, who paid particular attention to the role of the grain boundaries in plastic flow. The nonuniformit of the plastic deformation in microvolumes was also recorded by T.N. Gudkova and others, on the alloy KhN80T. N.F. Lashko pointed out the nonuniformity of the plastic deformation for a series of pure polycrystalline metals and one-phase alloys. In his later reports, P.O. Pashkov arrives at he conclusion that the nonuniformity of the distribution of the deformation along the individual grains has a significant effect on the strength and plastic characteristics of polycrystalline metals in the process of plastic flow. However, until now there has not existed any systematic investigation of the general rules of the microscopic nonuniformit of plastic deformation even though the real polycrystalline metals are extremely simple with regard to structure. In the present report, an attempt is made to study the micrononuniformity of the flow of polycrystalline metals by the method of statistical analysis of the variation of the frequency diagrams of the nonuniformity of the grains in the process of plastic deformation.

Chechulin, B. B.↗

NASA NTRS2014

Impact-Induced Chondrule Deformation and Aqueous Alteration of CM2 Murchison

Deformed chondrules in CM2 Murchison have been found to define a prominent foliation [1,2] and lineation [3] in 3D using X-ray computed tomography (XCT). It has been hypothesized that chondrules in foliated chondrites deform by "squeezing" into surrounding pore space [4,5], a process that also likely removes primary porosity [6]. However, shock stage classification based on olivine extinction in Murchison is consistently low (S1-S2) [4-5,7] implying that significant intracrystalline plastic deformation of olivine has not occurred. One objective of our study is therefore to determine the microstructural mechanisms and phases that are accommodating the impact stress and resulting in relative displacements within the chondrules. Another question regarding impact deformation in Murchison is whether it facilitated aqueous alteration as has been proposed for the CMs which generally show a positive correlation between degree of alteration and petrofabric strength [7,2]. As pointed out by [2], CM Murchison represents a unique counterpoint to this correlation: it has a strong petrofabric but a relatively low degree of aqueous alteration. However, Murchison may not represent an inconsistency to the proposed causal relationship between impact and alteration, if it can be established that the incipient aqueous alteration post-dated chondrule deformation. Methods: Two thin sections from Murchison sample USNM 5487 were cut approximately perpendicular to the foliation and parallel to lineation determined by XCT [1,3] and one section was additionally polished for EBSD. Using a combination of optical petrography, SEM, EDS, and EBSD several chondrules were characterized in detail to: determine phases, find microstructures indicative of strain, document the geometric relationships between grain-scale microstructures and the foliation and lineation direction, and look for textural relationships of alteration minerals (tochilinite and Mg-Fe serpentine) that indicate timing of their formation relative to deformation event(s). Preliminary Results: Deformed chondrules are dominated by forsterite and clinoenstatite with lesser amounts of Fe-Mg serpentine, sulfides, and low calcium pyroxene. Olivine grains are commonly fractured but generally show sharp optical extinction. The pyroxene, in contrast, is not only fractured but also often displays undulose extinction. In addition, the clinoenstatite is frequently twinned but it is unclear whether the twins are the result of mechanical deformation or inversion from protoenstatite [8]. EBSD work is currently ongoing to determine if areas of higher crystallographic strain can be imaged and mapped, and to determine the pyroxene twin orientations. In regards to alteration, we have found evidence for post-deformation formation of tochilinite and Mg-Fe serpentine indicating that aqueous alteration has indeed post-dated the deformation of the chondrules.

Hanna, R. D.↗

DOE OSTI2025

Pulse-by-pulse transient thermal deformation in crystal optics under high-repetition-rate FEL

Time-domain modeling of the thermal deformation of crystal optics can help define acceptable operational ranges across the pulse-energy repetition-rate phase space. In this paper, we have studied the transient thermal deformation of a water-cooled diamond crystal for a cavity-based X-ray free-electron laser (CBXFEL), either an X-ray free-electron laser oscillator (XFELO) or a regenerative amplifier X-ray free-electron laser (RAFEL), by numerical simulations including finite-element analysis and advanced data processing. Pulse-by-pulse transient thermal deformation of a 50 µm-thick diamond crystal has been performed with X-ray pulse repetition rates between 50 kHz and 1 MHz. Results for temperature and thermal deformation have been compared with the results of transient analysis using a continuous wave (CW) power loading. Temperature and thermal deformation results from pulse-by-pulse transient analysis vary with time about the results for the CW case for the same average power. The variation amplitude increases with pulse energy and decreases with repetition rate. When the repetition rate increases to infinity, both temperature and thermal deformation converge to the results for the CW case. Two critical time scales for the operation of crystal optics in a CBXFEL are (1) first-turn time, i.e. the time for the XFEL pulse to complete the first turn around the cavity so that the crystal sees the recirculated XFEL pulse, and (2) period-end time, i.e. the time that the next electron bunch arrives for the amplification, so that the crystal outcouples the amplified FEL power. For the same average power, simulation results show that the crystal thermal deformation seen by the XFEL beam decreases with repetition rate at the first-turn time of a 300 m-long cavity and increases with repetition rate at the period-end time. For the wavefront preservation requirement of the crystal optics, a pulse-energy versus repetition-rate phase space has been established. The upper bounds of the pulse energy at both first-turn and period-end times decreases with repetition rate, especially at the period-end time. The upper bound of the thermal deformation of the crystal at the period-end time for any repetition frequency can be estimated from the CW case. For a water-cooled diamond crystal of dimension 5 mm × 5 mm × 0.05 mm, the time to reach a quasi steady-state is about 50 ms for temperature and 50 µs for thermal deformation.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2021

Shear-based deformation processing of age-hardened aluminum alloy for single-step sheet production

Shear-based deformation processing by hybrid cutting-extrusion and free machining are used to make continuous strip, of thickness up to one millimeter, from low-workability AA6013-T6 in a single deformation step. The intense shear can impose effective strains as large as 2 in the strip without pre-heating of the workpiece. The creation of strip in a single step is facilitated by three factors inherent to the cutting deformation zone: highly confined shear deformation, in situ plastic deformation-induced heating and high hydrostatic pressure. The hybrid cutting-extrusion, which employs a second die located across from the primary cutting tool to constrain the chip geometry, is found to produce strip with smooth surfaces (S a < 0.4 μm) that is similar to cold-rolled strip. The strips show an elongated grain microstructure that is inclined to the strip surfaces – a shear texture – that is quite different from rolled sheet. Furthermore, this shear texture (inclination) angle is determined by the deformation path. Through control of the deformation parameters such as strain and temperature, a range of microstructures and strengths could be achieved in the strip. When the cutting-based deformation was done at room temperature, without workpiece pre-heating, the starting T6 material was further strengthened by as much as 30% in a single step. In elevated-temperature cutting-extrusion, dynamic recrystallization was observed, resulting in a refined grain size in the strip. Implications for deformation processing of age-hardenable Al alloys into sheet form, and microstructure control therein, are discussed.

36 MATERIALS SCIENCE↗

DOE OSTI2020

In Situ Synchrotron X-ray Diffraction Investigations of the Nonlinear Deformation Behavior of a Low Modulus β -Type Ti36Nb5Zr Alloy

The low modulus β-type Ti alloys usually have peculiar deformation behaviors due to their low phase stability. However, the study of the underlying mechanisms is challenging since some physical mechanisms are fully reversible after the release of the load. In this paper, the deformation behavior of a low modulus β-type Ti36Nb5Zr alloy was investigated with the aid of in situ synchrotron X-ray diffraction (SXRD) during tensile loading. The evolution of lattice strains and relative integrated diffraction peak intensities of both the β and α” phases were analyzed to determine the characteristics of the potential deformation mechanisms. Upon loading, the α” diffraction spots appeared at specific azimuth angles of the two-dimensional SXRD patterns due to the <110> fiber texture of original β grains and the selection of favorable martensitic variants. The nonlinear deformation behavior originated from a reversible stress-induced martensitic transformation (SIMT). However, the SIMT contributed a little to the large recoverable strain of over 2.0%, which was dominated by the elastic deformation of the β phase. Various deformation mechanisms were activated successively at different applied strains, including elastic deformation, SIMT and plastic deformation. Our investigations provide in-depth understandings of the deformation mechanisms in β-type Ti alloys with low elastic modulus.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Deformation band corrosion as a result of applied stress and cold-work in 304 stainless steel in simulated pressurized water reactor primary water conditions

Stainless steels like 304SS are commonly used in pressurized water reactor primary water environments due to their excellent resistance to stress corrosion cracking (SCC). However, SCC susceptibility has been observed in cold-worked 304SS. Cold-rolling introduces a high density of defects, such as deformation bands or dislocations, into the microstructure; applied stress, even if macroscopically below the yield stress, can result in regions with high localized stresses. Cold-worked and non-cold-worked samples were exposed to 360 °C simulated PWR primary water for 1500 h with and without active loading. Corrosion susceptibility of dislocations and deformation bands induced by cold-rolling and/or applied stress was studied using high-resolution (analytical) transmission electron microscopy. Deformation bands were generated in all specimens examined in the study. Penetrative oxidation was observed in some deformation bands in each specimen. The depth of penetrative deformation band oxidation frequently exceeded the depth of grain boundary oxidation in all specimens. However, deformation band oxides generally were narrowly confined to the deformation band plane. Highly Ni-rich regions were observed beyond all oxidation fronts. Surface oxides were thicker in the specimens exposed under active loading. In conclusion, the implications of these findings at surfaces for deformation bands intersecting stress corrosion crack paths are discussed.

EFTEM↗

DOE OSTI2025

Microstructure and CPO evolution of dynamically recrystallized olivine during complex deformation conditions: a full-field numerical modeling approach

The rheological properties of mantle rocks are strongly dependent on their crystallographic preferred orientation (CPO). Olivine CPO, defined by the orientation of seismically fast [100] axes parallel to flow direction, is also thought to be a dominant contributor to seismic anisotropy in the Earth's upper mantle. However, the amount of deformation needed to overprint a new CPO on a pre-existing fabric and the impact of the inherited CPOs on the transient microstructure evolution, remain unknown. This study employs a full-field numerical approach (VPFFT-ELLE) to explore the dynamic recrystallization and microstructural evolution of olivine polycrystalline aggregates under complex deformation conditions. We test four combinations of successive pure shear and simple shear boundary conditions. Findings indicate that inherited CPOs influence subsequent deformation in a manner dependent on the kinematic relationship between successive stages. In all cases, a minor strain increment (ε ∼0.3–0.6) is sufficient to erase the previous microstructure and CPO. However, when deformation conditions change dramatically (e.g., stretching direction changes orthogonally), the intensity of the new CPO developed is significantly lower and strain distribution are specially altered. During a transient strain stage, pre-existing microstructures undergo extensive reworking, especially when deformation conditions are changed dramatically, such as switching from simple shear to a pure shear condition with a parallel shortening direction relative to the stretching direction. We estimate the significance of these results in interpreting observations of seismic velocity anisotropy, concluding that P-wave seismic anisotropy is significantly and positively correlated with the evolution of olivine CPO with deformation history. This research underscores the transient nature of microstructural rearrangement in olivine aggregates and the necessity for caution in interpreting seismic anisotropy in regions with complex deformation histories, as inherited CPOs can influence current fabric development and induce deviation to the present deformation conditions.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Characterization of mechanical properties and deformation behavior of highly irradiated 316L stainless steel from target modules at the Spallation Neutron Source using digital image correlation analysis

Tensile specimens with irradiation doses ranging from approximately 0.7 to 7.6 displacements per atom (dpa) were fabricated from 316L samples removed from Spallation Neutron Source (SNS) target vessels after service. Tensile tests were performed in conjunction with digital image correlation (DIC) characterization, which permitted detailed analysis of the strain distribution and deformation behavior of the specimen gauge sections during testing. The results show, while considerable hardening (500–700 MPa increase in yield strength) occurred in the 316L SNS target material with increasing dose, appreciable ductility (19–23% total elongation) remained in the material after irradiation to 7.6 dpa in the mixed neutron/proton environment of the SNS target region. The DIC data showed the strain distribution and deformation behavior of all irradiated specimens were nonuniform during testing. Strain localization in the form of deformation bands or “hotspots” was observed during testing, and in some specimens, the bands propagated as deformation waves along the gauge section. The “traveling wave” deformation behavior affected the amount of elongation each specimen achieved, and the scatter in the elongation data was attributed to the large variation in deformation behavior observed among different specimens. Bands of localized strain, or deformation bands, oriented at specific angles were observed in two-dimensional plots of the strain distribution in the gauge sections of some specimens. Overall, this paper describes the experimental procedures, results, and deformation behavior of tensile specimens from SNS targets after service and illustrates the value of DIC characterization during tensile testing of irradiated materials.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Automated identification of deformation twin systems in Mg WE43 from SEM DIC

In this study, the application of machine learning and computer vision approaches to microscale deformation data for the automated identification of deformation twinning systems, and their associated twin area, is introduced. Deformation data was obtained during in-situ SEM compression testing of a WE43 Mg alloy using digital image correlation (DIC) modified for use with electron microscopy. A 5.7 mm × 3.4 mm area of interest was analyzed, generating ~100 million data points of deformation. Experimental twin trace directions were determined by applying k-means clustering, morphological thinning, and Hough transforms to the deformation data. The identification of deformation twinning was achieved by consideration of the twin trace direction, its strain value, and its evolution. The deformation map was divided into areas corresponding to individual active twin systems, enabling the analysis of microstructure dependence of deformation behavior and twinning activity. The performance of the proposed twinning identification approach was evaluated by accuracy, precision, and sensitivity metrics. The effect of the tuning parameters used in the algorithm on the performance is also discussed.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Multiscale Imaging of Nuclear Deformation at the Electron-Ion Collider

We show within the Color Glass Condensate framework that exclusive vector meson production at high energy is sensitive to the geometric deformation of the target nucleus at multiple length scales. Studying e+U collisions and varying the deformation of the uranium target, we demonstrate that larger deformations result in enhanced incoherent vector meson production cross sections. Further, different multipole deformation parameters affect different regions of transverse momentum transfer. Employing JIMWLK evolution to study the Bjorken-x dependence of our results, we find that the ratio of incoherent to coherent cross sections decreases with decreasing x, largely independently of the quadrupole deformation of the target. Comparing results for the same process using 20 Ne targets with 16 O targets, we find that differences in deformation are clearly visible in the incoherent cross section. These findings show that certain observables at the Electron-Ion Collider are very sensitive to nuclear structure. Consequently, deformations need to be taken into account when interpreting experimental results. More importantly, this also means that |t|-differential diffractive vector meson production could become a powerful tool, enabling the most direct measurements of nuclear structure at different length scales, ranging from nuclear deformation at low |t| to nucleon and subnucleon-size scales at higher |t|.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2021

Measurement of Deformation Heterogeneity During Shale Swelling Using Digital Image Correlation

Abstract Rock-fluid interactions in shale formations are one of the main sources of wellbore instability issues and inadequate stimulation performance. For better planning of fracturing operations and optimizing production from these reservoirs, it is important to understand the mechanisms behind these interactions. These issues are especially prevalent in clay-rich shales, such as Tuscaloosa Marine Shale, which is the subject of this study. Conventional techniques to quantify these shale-fluid interactions comprise of measuring swelling in powdered rock grains or measurement of deformation in the whole pieces of the core using a linear variable differential transformer and strain gages. However, the contribution from individual laminae to overall deformation cannot be evaluated using these methods. In this study, we developed an experimental setup to evaluate the spatial deformation in shale during interaction with water using digital image correlation (DIC). Deformation of two shale samples, with 34 wt% to 51 wt% clay content, was studied. White paint was used to generate a random speckle pattern on the specimen and then immersed in deionized water. The deformation process was captured using a digital camera and images were analyzed using DIC to quantify the deformation. The implementation of the DIC technique enables the visualization and quantification of spatial deformation in the specimen during interacting with water. The results show the localization of large strains in select laminations. The results provide a better understanding of shale deformation when interacting with water in comparison to traditional measurements that can provide only an average strain value.

Energy & Fuels↗

NASA NTRS2004

Associative Flow Rule Used to Include Hydrostatic Stress Effects in Analysis of Strain-Rate-Dependent Deformation of Polymer Matrix Composites

designing reliable composite engine cases that are lighter than the metal cases in current use. The types of polymer matrix composites that are likely to be used in such an application have a deformation response that is nonlinear and that varies with strain rate. The nonlinearity and the strain-rate dependence of the composite response are due primarily to the matrix constituent. Therefore, in developing material models to be used in the design of impact-resistant composite engine cases, the deformation of the polymer matrix must be correctly analyzed. However, unlike in metals, the nonlinear response of polymers depends on the hydrostatic stresses, which must be accounted for within an analytical model. By applying micromechanics techniques along with given fiber properties, one can also determine the effects of the hydrostatic stresses in the polymer on the overall composite deformation response. First efforts to account for the hydrostatic stress effects in the composite deformation applied purely empirical methods that relied on composite-level data. In later efforts, to allow polymer properties to be characterized solely on the basis of polymer data, researchers at the NASA Glenn Research Center developed equations to model the polymers that were based on a non-associative flow rule, and efforts to use these equations to simulate the deformation of representative polymer materials were reasonably successful. However, these equations were found to have difficulty in correctly analyzing the multiaxial stress states found in the polymer matrix constituent of a composite material. To correct these difficulties, and to allow for the accurate simulation of the nonlinear strain-rate-dependent deformation analysis of polymer matrix composites, in the efforts reported here Glenn researchers reformulated the polymer constitutive equations from basic principles using the concept of an associative flow rule. These revised equations were characterized and validated in an experimental program carried out through a university grant with the Ohio State University, wherein tensile and shear deformation data were obtained for a representative polymer for strain rates ranging from quasi-static to high rates of several hundred per second. Tensile deformation data also were obtained over a variety of strain rates and fiber orientation angles for a representative polymer matrix composite composed using the polymer.

Goldberg, Robert K.↗