SEARCH · Search NASA

Results for “ductile failure”

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 181 records · Page 10

All sources NASA NTRS DOE OSTI

DOE OSTI2025

Development and Evaluation of Embrittlement Resistant Alloys for Advanced LWR Cladding

The primary challenge preventing the deployment of reactor designs that leverage wrought FeCrAl as an advanced light-water reactor (LWR) cladding is irradiation hardening and embrittlement. Wrought FeCrAl alloys experience a loss of post-irradiation ductility and fracture toughness under low-temperature neutron irradiation (< 350°C) resulting from the combined effects of dislocation loop formation and the irradiation-enhanced precipitation of Cr-rich alpha-prime precipitates throughout the microstructure. Over the past decade, significant improvements in our understanding regarding the effect of Cr and Al content have been enabled through neutron irradiations, but even optimized wrought alloys such as C26M remain vulnerable to brittle failure during storage, transportation, and handling following irradiation. This report summarizes multiple irradiation campaigns initiated over the past 7 years and provides recent insights into the effect of (1) minor alloying composition, (2) alloy processing strategy, (3) crystal structure, and (4) the use of advanced oxide dispersion strengthened (ODS) alloys. The first irradiation campaign irradiated body-centered cubic FeCrAl alloy C26M with and without elements such as Mo and Y. It also included face-centered cubic alumina-forming austenitic (AFA) alloys that have a steeper neutronic penalty but that have far superior high-temperature strength than wrought FeCrAl. Finally, this campaign compared conventional wrought C26M with the same material produced using modern powder metallurgical hotisostatic pressing (PM-HIP). The second irradiation campaign, initiated in 2018, irradiated wrought and FeCrAl-ODS materials up to 50 dpa to assess their irradiation resistance to high-doses. The results of this work indicate that wrought C26M suffers significant degradation following neutron irradiation at LWR-relevant temperatures regardless of Mo and Y content. The PM-HIP variant appears to be more resilient to irradiation-induced ductility loss in comparison with wrought variants but still loses almost all ductility by 8 dpa. Notably, the AFAs retained at least 5% total elongation after irradiation at the same dose and temperature condition, although additional deterioration may be expected at higher fluence levels. FeCrAl-ODS materials show the greatest promise as a transformative longer-term accident-tolerant fuel (LT-ATF) cladding material. The extruded 106ZY10C alloy retained 10% total elongation after 16 dpa irradiation and retained 8% total elongation after 50 dpa. Additional challenges with FeCrAl-ODS alloys also remain, including optimization of end cap joining methodologies, enhancement of fracture toughness, scaling production to prove economic viability, and optimizing post-pilger heat treatments to maximize ductility and irradiation resistance. This series of irradiations demonstrates the efficacy of the LWR testbed available within the United States for the rapid irradiation and down-selection of LT-ATF candidates. As the country rapidly accelerates its timeline for the deployment of advanced reactor concepts, the effective utilization of the High Flux Isotope Reactor for separate-effects style irradiations should continue to be prioritized to answer the final questions pertaining to LT-ATF candidates necessary for the deployment of advanced boiling water reactors and small modular reactors.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2023

Interfacial microstructure and mechanical properties of rotary inertia friction welded dissimilar 422 martensitic stainless steel to 4140 low alloy steel joints

In this work, dissimilar rotary inertia friction welds between 422 martensitic stainless steel and 4140 martensitic low-alloy steel were made to fabricate prototype heavy-duty diesel engine pistons. The influence of the inertia friction welding process and post weld heat treatment (PWHT) temperature on the interfacial microstructure evolutions and corresponding effects on mechanical properties of the 422/4140 welds were evaluated in detail. Carbon diffused from the 4140 side to the 422 side during PWHT at 650 °C for 1.5 h, causing the formation of a hard carbide-rich layer on the 422 side, and a softer but discontinuous C-depleted layer the 4140 side. PWHT at 700 °C for 1.5 h greatly accelerated C diffusion across the interface relative to 650 °C, resulting in a thicker hard carbide-rich layer and a relatively thick and continuous layer of coarse C-depleted grains (ferrite) on the 4140 side. In addition, the PWHT temperature greatly influenced the tensile properties and fracture behavior of the welds, with the 650 °C PWHT-ed samples failing predominately in a ductile manner in the 4140 heat affected zone during tensile testing. Conversely, the 700 °C PWHT specimens exhibited a strength reduction compared with the 650 °C PWHT specimens because of additional coarsening of the interfacial ferrite layer and softening of the base materials during PWHT, with brittle fracture between the hard and soft layers the predominate failure mechanism. Based on the findings, a reduced PWHT temperature and/or time, minimizing the hardness differential of the base metals, and pre-heating the 422 steel prior to welding are the potential pathways to achieve a more optimal balance between desirable tempering and stress relief of the weld microstructure and undesirable C migration across the weld interface, and to reduce the strength mismatch across the weld.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Considerations for Thermal Annealing of Zr-Alloy Cladding During Dry Storage

In January 2025, the U.S. Department of Energy (DOE) sponsored a technical workshop with fuel vendors that provided a forum for increased collaboration on backend fuel cycle research. The workshop reviewed observations of thermal annealing of irradiated zirconium alloys in simulated dry storage conditions and discussed implications to the industry’s interest in reducing wet storage to optimize operational flexibility and the expected trend of increasing discharge burnup (and decay heats), which could lead to an increase in dry storage temperatures. One approach to accommodate increased decay heats in dry storage is to increase the regulatory temperature limit during dry storage, which is now 400°C. However, this could lead to thermal annealing of the cladding, which will tend to increase creep rates, creep strains, and ductility while decreasing yield strength. These considerations are compounded by bonding between the pellet and cladding at high burnup, which results in the pellet carrying more load during fuel rod deformations, especially in bending, which is the dominant deformation phenomenon in canister drop analyses. Because the U.S. Nuclear Regulatory Commission (NRC) recommends yield strength as a primary failure criterion for accident analyses in storage and transportation, particularly for canister drop scenarios, the purpose of the workshop was to develop options for alternative failure criterion that could replace yield strength in canister drop analyses. Topics discussed were (1) the regulatory framework, (2) the effect of thermal annealing on microhardness and tensile properties of cladding materials, (3) the effect of thermal annealing on fuel rod failure during bending, bending fatigue, and pinch loading, and (4) an alternative failure criterion for canister drop analyses. This paper provides a summary of the key discussions and outcomes of the workshop

Cantonwine, Paul [ORNL] (ORCID:0009000522247033)↗

DOE OSTI2026

Hydrogen embrittlement and mechanical response of 304L steel with ZrC additions

While stainless steels are widely used for hydrogen storage infrastructure, they can still be vulnerable to hydrogen embrittlement justifying the need to further improve their hydrogen resiliency. Here, we investigate the potential for transition metal carbide additions to improve the hydrogen compatibility of austenitic stainless steels. ZrC nanoparticles were dispersed in contents of 0.01–10 wt% in 304 L stainless steel powder, mixed via high energy ball milling, and subsequently consolidated using direct current sintering. To assess hydrogen compatibility, the tensile properties of similarly processed 304 L without ZrC nanoparticles were compared to 304 L with the ZrC additions; both materials were evaluated prior to and after hydrogen exposure (non-charged and H-precharged, respectively). Depending upon the ZrC phase fraction, the yield strengths varied from ∼325 to 560 MPa in the non-charged condition and from ∼375 to 550 MPa in the H-precharged condition. Strain at failure varied from ∼5 to 90 % and from ∼5 to 35 % in the non-charged and hydrogen-precharged conditions, respectively. Results from stress-strain profiles demonstrate limited efficacy of ZrC as a method to mitigate hydrogen embrittlement entirely but does demonstrate the potency of ZrC inclusions as strengthening addition to 304 L alloys without a loss of ductility.

08 HYDROGEN↗

DOE OSTI2021

Temperature and time effects of post-weld heat treatments on tensile properties and microstructure of Zircaloy-4

Opportunities exist to expand the application of Zircaloy-4 (Zry-4) into lower-temperature (<100°C) applications. Welded areas within these structures are potential failure points and post-weld heat treatments (PWHTs) are not yet standardized for application in this temperature range. Zry-4 tungsten inert gas (TIG) welds were given PWHTs from 450-900°C with hold times from 0.5-48 hours to investigate changes to tensile properties and microstructure. Treatment of 800°C for 1 hour was found to produce the most ductile material, measured by total elongation of the tensile bar (16.5%). Furthermore, both PWHT time and temperature were observed to increase total elongation, except in extreme (>800°C or >18hours) cases, but the effect of temperature was stronger. The second order cumulative annealing parameter shows a trend with tensile properties. Average grain sizes in the fusion zone and heat affected zone did not change under any of the PWHTs until the development of an undesirable blocky-alpha phase, which was only observed to form in the heat affected zones for hold times greater than 18hr at 800°C.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Internal short circuit and failure mechanisms of lithium-ion pouch cells under mechanical indentation abuse conditions: An experimental study

Electromechanical structural integrity and thermal stability dictate the safety performance of lithium-ion batteries. Progressive deformation and failure across microscopic and macroscopic lengths scales that are responsible for internal short circuit (ISC) in lithium-ion cells under mechanical abuse conditions remains elusive. In this study, a series of indentation tests were conducted on lithium-ion cells with different capacities up to the occurrence of ISC. The external response and internal configuration of these cells were investigated. It is discovered that cells with different capacities and state of charges exhibited different behaviors. Maximum temperature, which is often regarded as the most important parameter related to thermal runaway (TR), varied considerably due to the complicated contact configurations. X-ray computed tomography (XCT) showed that ISC was a collective result of shear band or other strain-localization modes in the electrode assembly, shear offsets in the granular coatings of electrodes, and the accompanying ductile fracture in the metal foils. We believe that the irregular strain-localization modes (kinks, cusps, and buckles), radical mismatches in mechanical properties of different layers, and geometric features of the indenter eventually lead to the tearing/puncture of cell separator at various locations. Furthermore, the results could provide useful guidance for the micromechanical modeling of lithium-ion cells.

25 ENERGY STORAGE↗

DOE OSTI2020

Dynamic Tensile Characterization of Thin-Sheet Brittle Metallic Materials

Refractory metals are favorable materials in applications where high strength and ductility are needed at elevated temperatures. In some cases, operating temperatures may be near the melting point of the material. However, as temperature drops, refractory metals typically undergo a significant mechanical response change - ductile-to-brittle transition. These materials may be subjected to high strain rate loading at an ambient temperature state, such as an impact or crash. Knowledge of the high rate material properties are essential for design as well as simulation of impact events. The high rate stress-strain behavior of brittle metallic materials at ambient temperature is rarely studied because of experimental challenges, particularly when failure is involved. Failure typically occurs within the non-gage section of the material, which invalidates any collected stress-strain information. Here, a method to determine a specimen geometry which will produce failures in the gage section is presented. Pure tungsten in thin-sheet form was used as a trial material to select a specimen geometry for high rate Kolsky tension bar experiments. A finite element simulation was conducted to derive a strain correction for more accurate results. The room temperature stress-strain behavior of pure tungsten at a strain rate of 24 s –1 is presented. The outcome of this experimental technique can be applied to other brittle materials for dynamic tensile characterization.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Development and Evaluation of Embrittlement Resistant Alloys for Advanced LWR Cladding

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2021

Thermomechanical Microstructural Predictions of Fracture Nucleation of Zircaloy-4 Alloys With δ and ε Hydride Distributions

Abstract A crystalline dislocation-density formulation that was incorporated with a nonlinear finite-element (FE) method was utilized to understand and to predict the thermomechanical behavior of an hexagonal closest packed (h.c.p.) zircaloy system with hydrides with either face-centered cubic (f.c.c.) or body-centered cubic (b.c.c.) hydrides. This formulation was then used with a recently developed fracture methodology that is adapted for finite inelastic strains and multiphase crystalline systems to understand how different microstructurally based fracture modes nucleate and propagate. The interrelated microstructural characteristics of the different crystalline hydride and matrix phases with the necessary orientation relationships (ORs) have been represented, such that a detailed physical understanding of fracture nucleation and propagation can be predicted for the simultaneous thermomechanical failure modes of hydride populations and the matrix. The effects of volume fraction, morphology, crystalline structure, and orientation and distribution of the hydrides on simultaneous and multiple fracture modes were investigated for radial, circumferential, and mixed distributions. Another key aspect was accounting for temperatures changes due to the effects of thermal conduction and dissipated plastic work and their collective effects on fracture. For hydrided aggregates subjected to high temperatures, thermal softening resulted in higher ductility due to increased dislocation-density activity, which led to higher shear strain accumulation and inhibited crack nucleation and growth. The predictions provide validated insights into why circumferential hydrides are more fracture-resistant than radial hydrides for different volume fractions and thermomechanical loading conditions.

Engineering↗

DOE OSTI2025

Understanding Geometry and Microstructure Interactions In LPBF By Linking Lab Scale Studies To Real Part Case Examples

The mechanical properties derived from simple tensile tests are uniquely important in the design and qualification of load bearing metallic components. The tensile properties in standards for wrought metallic materials are generally accessible for design and simulation engineers, but this is not the case for additively manufactured metals. This work investigates the influence of tensile specimen geometry on the mechanical properties of laser powder bed fusion (LPBF) additively manufactured Ti-6Al-4V, particularly in relation to properties measured from specimens excised from an exemplar part. A comprehensive analysis was conducted across various specimen geometries, considering factors such as thermal history, cross-sectional area, shape, and surface roughness. Key findings reveal that sample size, particularly cross-sectional area, significantly affects reported tensile properties, with ASTM E8 flat and round specimens exhibiting differences in elastic modulus (13%), yield strength (17%), ultimate tensile strength (UTS) (14%), and elongation to failure (11%). Additionally, surface roughness was found to have a limited impact on ASTM round geometries, but it becomes critical in thin-walled and small high-throughput samples. The ASTM flat samples closely matched the properties of samples excised from the exemplar part, underscoring the necessity of testing witness samples that accurately represent end-use conditions. Furthermore, mechanical properties of samples built within the stitch zone of the exemplar part demonstrated reduced ductility, highlighting the importance of laser alignment and qualification in multi-laser additive manufacturing processes. Overall, this study emphasizes the need for careful consideration of specimen geometry and testing conditions to ensure accurate reporting of mechanical properties in LPBF Ti-6Al-4V.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Burst characteristics of advanced accident-tolerant FeCrAl cladding under temperature transient testing

Here assessment of burst characteristics of accident-tolerant fuel (ATF) claddings is essential to evaluate the safety margins of nuclear reactors, and better understanding can enable accelerated licensing for reactor concepts that include the new materials. Therefore, this study investigated the burst behavior of an ATF candidate of C26M, which is an iron–chromium–aluminum alloy (FeCrAl) under transient testing like the simulated loss-of-coolant accident (LOCA) conditions, except the water-quenching phase, in light-water reactors (LWRs). The effect of LOCA specimen length was assessed in terms of post-burst tube parameters. No critical length effect was determined on the burst pressure, burst location, and burst size measurements. Burst temperature showed larger variation likely due to its measurement approach used in this study. The post-test diametral strain was identified as the critical parameter to reduce the specimen length as compared to tube burst length or width. Postmortem optical metrology and digital image correlation were employed to determine the local strain-state during the simulated LOCA, which showed the loading path was close to equibiaxial conditions in regions away from the burst location, rather than internally pressurized conditions (or “plane-strain” tension). Pst-test microstructural characterizations of the FeCrAl revealed that ductile damage was present at the edge of the outer radial surface while the rest of the material was ruptured via cleavage at LOCA burst temperatures. Furthermore, internal grain boundary cracks were observed at locations away from the tube burst region. This behavior was considered to occur during the cooling down period of the simulated LOCA test. Overall, this study aimed to provide essential data for fuel performance code development by considering micromechanics of the deformation and failure.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Ductile adhesive elastomers with force-triggered ultra-high adhesion strength

Elastomers play a vital role in many forthcoming advanced technologies in which their adhesive properties determine materials’ interface performance. Despite great success in improving the adhesive properties of elastomers, permanent adhesives tend to stick to the surfaces prematurely or result in poor contact depending on the installation method. Thus, elastomers with on-demand adhesion that is not limited to being triggered by UV light or heat, which may not be practical for scenarios that do not allow an additional external source, provide a solution to various challenges in conventional adhesive elastomers. Herein, we report a novel, ready-to-use, ultra high-strength, ductile adhesive elastomer with an on-demand adhesion feature that can be easily triggered by a compression force. The precursor is mainly composed of a capsule-separated, two-component curing system. After a force-trigger and curing process, the ductile adhesive elastomer exhibits a peel strength and a lap shear strength of 1.2 × 10 4 N m -1 and 7.8 × 10 3 kPa, respectively, which exceed the reported values for advanced ductile adhesive elastomers. The ultra-high adhesion force is attributed to the excellent surface contact of the liquid-like precursor and to the high elastic modulus of the cured elastomer that is reinforced by a two-phase design. In conclusion, incorporation of such on-demand adhesion into an elastomer enables a controlled delay between installation and curing so that these can take place under their individual ideal conditions, effectively reducing the energy cost, preventing failures, and improving installation processes.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Small Punch Testing of Molybdenum-99 Targets

Northstar Medical Radioisotopes is developing an accelerator-based method to produce 99 Mo, which is a parent isotope of the commonly used 99m Tc medical isotope. The Mo targets being designed for the accelerator will be produced from enriched 100 Mo, also known as aMo . Pressed and sintered powder feedstock is used to fabricate aMo targets, producing 29 mm disk-shaped targets. The targets are subjected to 1–6 days in line of an electron beam with subsequent dissolution of the disk to retain the 99 Mo, which decays to 99m Tc at radio-pharmacies. The press and sinter method is advantageous because the inherent porosity produced by this method enables increased surface area and therefore increased flow of dissolution media, decreasing the dissolution time and reducing the need for a highly acidic media. Although porosity aids in dissolution, it reduces the mechanical strength and ductility. Targets require good mechanical integrity when subjected to the conditions in the accelerator. Therefore, Northstar is seeking methods to rapidly test disk samples after fabrication to assure mechanical performance metrics are achieved. This report details the design and testing of a small punch test (SPT) that accommodates the 29 mm disk. Initial data were used to relate the SPT data to tensile properties, such as the yield strength (YS), ultimate tensile strength (UTS), and total elongation to failure. Although the SPT has been established as a somewhat reliable method for testing metallic materials, few studies have applied the SPT to refractory materials such as Mo. Based on tensile testing performed at Oak Ridge National Laboratory on different Mo samples, correlation between the Mo tensile and SPT properties could be performed, establishing a standard calibration that could be applied to other Mo samples. To test the efficacy of the SPT with Mo, multiple different disk batches were fabricated under different conditions (e.g., pressure, lubricant) with commercially available pure Mo powder. Generally, only a UTS could be well defined because the press and sinter disks failed under brittle fracture, making it difficult to determine the YS and elongation. Compared with disks fabricated with aMo powder, the aMo samples underperformed their pure nat Mo counterparts. This report summarizes the current status of the SPT, but further evaluation is needed before it can be applied as a reliable quality assurance tool.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

DOE OSTI2022

Preliminary Study on Machining of Additively Manufactured Ti-6Al-4V

We report additively manufactured metals differ from their conventionally produced counterparts due to the inherent material inhomogeneity, porosity, and thermal stress induced by the process. These differences make the machining of additively manufactured metals more difficult and cause premature tool failure or unexpected surface finish at certain conditions. This study takes the first step to investigate and identify the causes of these issues, particularly for Ti-6Al-4V. Printed and wrought samples, as well as heat treatment effect, are compared in a dry cutting condition at a cutting speed of 90 m/min in terms of cutting power, vibration, temperature, and produced surface finish. The results show a lower cutting power and more vibration for as-printed Ti samples, indicating a less ductile microstructure and inclusion of pores. Heat treatment can eliminate these phenomena. There is no significant difference found in the produced surface finish at the current cutting condition.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Investigation of Machinability of Additively Manufactured Ti-6Al-4V

Additively manufactured metals differ from their conventionally produced counterparts due to the inherent material inhomogeneity, porosity, and thermal stress induced by the process. These differences make the machining of additively manufactured metals more difficult and cause premature tool failure or unexpected surface finish at certain conditions. This study takes the first step to investigate and identify the causes of these issues, particularly for Ti-6Al-4V. Printed and wrought samples, as well as heat treatment effect, are compared in a dry cutting condition at a cutting speed of 90 m/min in terms of cutting power, vibration, temperature, and produced surface finish. The results show a lower cutting power and more vibration for as-printed Ti samples, indicating a less ductile microstructure and inclusion of pores. Heat treatment can eliminate these phenomena. There is no significant difference found in the produced surface finish at the current cutting condition.

Raval, Jay↗

DOE OSTI2025

Utilizing machine learning to predict tensile ductility and yield strength of CoNiV-based multi-principal elements alloys

This study explores the use of machine learning (ML) as a computational tool to accelerate the design of multi-principal element alloys (MPEAs) with improved tensile elongation. An ML model was trained using available experimental data from the literature along with theoretically derived features to predict yield strength (YS) and ductility. A subset of ML-predicted compositions—CoNiVFe, CoNiVTi, CoNiVTiFe, and CoCrNiVTi—was synthesized and evaluated through tensile testing. The ML model underpredicted YS by approximately 20–30 % and overpredicted ductility by 60–70 % for Ti-containing alloys. Microstructural analysis revealed that Ti segregation at interdendritic regions contributed to early fracture, leading to discrepancies in ductility predictions. Ti segregation at these regions likely drives the increased YS due to segregation strengthening. In contrast, the CoNiVFe alloy showed good agreement with both experimental YS and elongation, with prediction errors of ∼10.2 % and ∼20.7 %, respectively. Microstructural characterization revealed minimal segregation in this alloy, suggesting that the ML model can reliably predict the properties of alloys with little to no segregation. These findings highlight the capability of ML in predicting YS with good accuracy but underscore its limitations in capturing defect-driven failure mechanisms such as segregation-induced embrittlement.

36 MATERIALS SCIENCE↗

DOE OSTI2022

A Comparative Study on Representativeness and Stochastic Efficacy of Miniature Tensile Specimen Testing

Here, in this article, a miniature dog bone tensile coupon design was tested against the existing ASTM standard specimen design. Specimens were prepared from commercially sourced austenitic stainless steel 304 alloy, and a defect-ridden additively manufactured 304L alloy was studied. By utilizing a tensile specimen design that is 1/230th volume of the smallest ASTM E8-04(2016), Standard Test Methods for Tension Testing of Metallic Materials, dog bone specimen, coupled to a digital image correlation (DIC) setup, case studies were performed to compare tensile property measurements and strain field evolution. Whereas yield strength measurements were observed to be similar, post-yield, the ultimate strength measurements and ductility measurements from the miniature specimens were observed to be higher than the ASTM specimen design. Although the strength measurements were comparable, the strain evolution was found to differ in the miniature specimens. Studies to assess effects of varying thickness and defect population were also pursued on the miniature tensile specimen. From the DIC strain field estimations, the peak local strain values at ultimate tensile strength were observed to be increasing with reducing specimen thickness. Testing of defect ridden stainless steel revealed the sensitivity to failure through strain localization and the influence of defect size was captured in the strength measurements.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Geodyn Material Library: Pseudocap models for dry porous tocks

This report describes the second edition of the Pseudocap Strength models for porous rocks implemented in GEODYN material library. The first model was developed in 2007 and calibrated for concrete. Then, the model parameters were calibrated based on triaxial tests reported for limestones and sandstones of various porosities. In these models some key parameters were chosen as functions of the reference porosity,Φ. Since then multiple modifications were implemented in the model, therefore, it has been recalibrated for some common porous materials such as limestones, sandstones, alluvium, tuffs and granite. Two types of models are described in this repot. The first type (called Pseudocap Model or PM) is for rocks from a specific location. Parameters were calibrated for several specific geologic materials. The second type (called Generic Pseudocap Model or GPM) is useful for the sites where only basic information (rock type, porosity) is available. Generic models include built-in correlations between porosities and other mechanical properties observed for certain rock types. The models of both types were validated by comparing not only to quasi-static triaxial tests for these materials but also to shock Hugoniot data and spherical explosion data for some materials. All models were derived in the frame of isotropic plasticity. They are designed to be used in explicit finite element/difference codes. Tangent stiffness tensor is not provided but can be calculated numerically for the model to be used in implicit finite element codes. For an isotropic material the stress can be decomposed into volumetric and deviatoric parts. The volumetric part is modeled using an Equation of state (EOS) which calculates the pressure and the bulk sound speed as functions of the internal specific energy and density. Here a simple, Mie-Gruneisen EOS is presented, but tabulated EOS (LEOS) provided by the library can be used as well. The stress is limited by the yield surface which depends on three invariants of the stress tensor and specific internal energy. In addition, to capture the strain-rate dependence a simple multiplier is used for the yield surface which depends on the equivalent plastic strain rate. The failure surface (the ultimate yield, Y f , defined later) is chosen in the Hoek-Brown form, commonly used in rock mechanics. It includes measurable parameters such as Unconfined Compressive Strength (UCS) as well as scale parameters characterizing the quality of the rock such as GSI (Geologic Strength Index). Thus, even though the model is calibrated for small samples it offers a way to extrapolate the strength to the field scale using geological characterization of the rock mass. The model captures effects of brittle-ductile transition in rocks by introducing a cap multiplier to the yield function. The rate of dilatancy (bulking) is proportional to the slope of the yield surface affected by the cap. Therefore, it takes place only at low confinements when the pressure is less than the brittle-ductile transition pressure, P BD . On the contrary, the porous compaction takes place at pressures higher than P BD . The cap moves as the porosity is compacted or new porosity is generated due to dilatancy. The porous compaction is modeled using an evolution equation which includes deviatoric stress so that the onset of compaction corresponds to the cap surface. The model captures effects of shear-enhanced compaction which is an important for porous rocks. Section 2 describes the modeling framework and Section 3 presents the model calibration procedure. Section 4 compares experimental data for various rocks versus model predictions. The model parameters used for this comparison are given in Appendix. The files with material constants are available with the latest GEODYN material library distribution.

58 GEOSCIENCES↗