Ratchet Growth Research Articles

Strain Measurement on a PBX during Temperature Cycling Using Fibre Bragg Gauges

AbstractThe anisotropic and irreversible expansion properties of polymer‐bonded explosives (PBX) can significantly influence the utility and reliability of associated equipment. The physical state of PBX under temperature cycling affects the strain distribution across the surface of cylindrical specimens. This strain is indicative of the irreversible growth and anisotropic expansion of the specimens. In this study, fiber Bragg grating sensors are employed to monitor the strain of PBX throughout the temperature cycling process, and our focus was on analyzing the changes in anisotropy and strain distribution during the cycle. The relationships between strain, temperature, material properties, and differences among various materials are examined. Experimental results indicate that the strain along the height and radial directions of the PBX specimens displayed a monotonic gradient distribution, increasing progressively in areas of higher density. TATB‐based PBX exhibited anisotropic expansion throughout the temperature cycling, with the degree of anisotropy increasing during heating and decreasing upon cooling. Conversely, HMX‐based PBX showed greater expansion in the height direction during both the heating and cooling phases, but it did not display noticeable anisotropy following the temperature cycling. At the highest temperature‐holding stage (100°C), the HMX‐based PBX was isotropic. The extent of strain in PBX was correlated with the thermal expansion coefficient of the crystal, although the final degree of expansion was not dependent on the initial range of strain. The ratchet growth of TATB‐based PBX was approximately 31 μϵ greater than that of HMX‐based PBX.

Multiscale numerical investigation of ratchet growth damage effects in PBX 9502

AbstractThis paper presents results of numerical experiments conducted on the high explosive PBX 9502 to investigate how recently observed grain‐scale damage mechanisms of ratchet growth [1] affect uniaxial compression measurements. Simulations are multiscale in the sense of directly resolving grains, pores, cracks, and grain‐interfaces based upon scanning electron microscope (SEM) images of damaged and undamaged samples. The combined finite‐discrete element method (FDEM) is utilized to resolve both grain‐scale microfracture and elastoplastic deformation of solid grains. Pristine (undamaged) and damaged microstructures are compared in simulation of unconfined compression tests of the same material from the literature. The simulation results show the observed microscale mechanisms of damage, specifically microfracture predominantly around and sometimes through grains and crack‐associated pore growth, can well‐explain the effective degradation of strength and stiffness observed in the laboratory measurements.

Mechanical and thermomechanical properties of an LLM‐105 based PBX high explosive with and without accelerated aging

AbstractIn this paper we present measurements and analysis on the mechanical and thermomechanical properties of the LLM‐105 based plastic bonded high explosive RX‐55‐DQ. Specifically we present uni‐axial compression, and thermal measurements (CTE and ratchet growth), and for some of the measurements we provide a comparison to measurements on TATB‐based PBX 9502. We also present the same mechanical property measurements performed on RX‐55‐DQ samples that underwent accelerated aging.

Modeling Ratchet Growth as Porosity Creep

Irreversible thermal cycling growth (or ratchet growth) of insensitive explosive formulations has been known for years. Traditionally it’s attributed to material texture and to anisotropic thermal expansion. Although this understanding has been accepted for a long time, we’re not aware of any model on the macroscale that connects these material properties to ratchet growth behavior. Thompson et al. [1] have observed that they get growth not just from thermal cycling, but also from a long hold time of the material sample at high temperature, and that such growth resembles creep response. Following their findings we propose here a predictive model for ratchet growth on the macroscale, where we assume that when temperature is increased, growth comes about by porosity (or volume) creep. We model ratchet growth by assuming that: 1) increasing temperature decreases strength in tension (negative pressure), causing the porosity in the part of the material that is in tension to creep (slowly increase in volume); and 2) increasing temperature increases the internal pressure/tension fluctuations caused by thermal expansion anisotropy, thereby enhancing the rate of porosity creep and ratchet growth. We write down equations for porosity creep and the resulting ratchet growth, and we demonstrate that our modeled ratchet growth results are similar to test data. We do not calibrate the free parameters of our model to reproduce specific data, as we do not own such data

Modelling of Ratchet Growth in TATB‐Based Charge under Thermal Cycling

AbstractThe TATB‐based explosives undergo irreversible volume growth upon a series of cyclic thermal loading known as ratchet growth and have been extensively studied. In the past, experimental elucidation of this phenomenon has focused on irreversible expansion as a function of the number of thermal excursions over a given temperature range, where growth is asymptotic with increasing cycle number. In this paper, we find that the ratchet growth of TATB‐based charge evolves associated with its dimension, and demonstrate that the growth can be modeled by a force‐thermal coupled calculation method. We have measured the strain response of four various size specimens, and the results show that irreversible strain on the smaller specimen grows more significantly and rapidly. Based on the equivalent relaxation model in which the relaxation stresses are regarded as functions of temperature and temperature gradient, we develop a force‐thermal coupled method for calculating the irreversible deformation. The relaxation model parameters were calibrated by comparing the calculations with the experimental measurements. We propose that it is the thermal expansion effect rather than thermal stress, which plays a dominant role in irreversible deformation. Further analysis indicated that the size effect of ratchet growth was not caused by temperature gradient, but was positively correlated with thermal excursions. The size effect of temperature distribution in the process of equivalent stress relaxation may be responsible for the size effect ratchet growth of TATB‐based charges. Such tests and analytical models should help to understand and predict the ratchet growth response for TATB‐based charges.

Coefficient of Thermal Expansion Evolution during Ratchet Growth of PBX 9502 and Neat TATB

AbstractThe Plastic‐Bonded Explosive (PBX) 9502 is comprised of the insensitive high explosive TATB (triamino trinitrobenzine) crystals coated in FK‐800 polymer binder and isostatically pressed. The TATB crystals have a graphitic, plate‐like morphology and possess significant thermal and mechanical anisotropy. Compactions of neat TATB or TATB‐based composites (like PBX 9502) have been shown to have TATB crystals that are oriented during the pressing process giving rise to TATB texture and resulting in micro‐ and macro‐scale anisotropy of the compaction. Thermal cycling of the compactions results in irreversible volume expansion (or ratchet growth) likely by creating stress points on the microscale. However, the actual mechanism behind this expansion is not fully understood. Previous characterization of the ratchet growth phenomenon has focused on the magnitude of the irreversible strain as measured before and after a thermal cycle. In the work presented here, we analyze the evolving thermal expansion behavior during the ascending and descending temperature ramps and compare differences observed due to the presence/absence of binder in the compaction.

Multiscale investigation of the microstructural mechanisms driving ratchet growth in PBX 9502

ABSTRACT The high explosive PBX 9502 undergoes irreversible expansion during thermal cycling (“ratchet growth”). Recent innovations in thermomechanical modeling via homogenization strategies are beginning to incorporate mesoscale information such as grain size, total porosity, and spatial distribution of voids and cracks. To generate a complete experimental data set to challenge and inform these models, PBX 9502 pellets were thermally cycled, cross-sectioned using ion polishing, and imaged in high resolution with scanning electron microscopy. Ratchet growth was found to drive expansion through microcracking. Microcracks were affected by agglomeration of crystals within the PBX. Virgin material showed greater ratchet growth than recycled material.

Coefficient of Thermal Expansion during Ratchet Growth of TATB Compactions

AbstractTriamino trinitrobenzene (TATB) is an insensitive high explosive, meaning that it is quite immune from accidental detonation and only performs in appropriately engineered configurations. While this is advantageous for applications, the TATB crystal is graphitic and possesses significant thermal and mechanical anisotropy. Compactions of TATB crystals, with or without binder, have been shown to have oriented TATB crystals that relate to the pressing geometry and process, and this TATB texture necessarily imparts microscale and macroscale anisotropy to the compaction. By a mechanism not fully understood, thermal cycling results in irreversible volume expansion (also called ratchet growth) of the compaction likely by creating stress points on the microscale. Changes in density caused by thermal cycling can certainly effect the explosive performance. Our past characterization of the ratchet growth phenomenon has focused on the magnitude of the irreversible strain as measured before and after a thermal cycle. In the work presented here, we analyze the evolving thermal expansion behavior during the ascending and descending temperature ramps, providing further insight into the material changes taking place during the ratchet growth phenomenon.

A thermo-elastoplastic self-consistent homogenization method for inter-granular plasticity with application to thermal ratcheting of TATB

A novel thermo-elastoplastic self-consistent homogenization model for granular materials that exhibit inter-granular plasticity is presented. The model, TEPSCA, is made possible by identifying a new inter-granular plastic Eshelby-like tensor. A micromechanical model of interfacial yielding between grains of a Mohr–Coulomb type is provided, which is relatable to the description of imperfect interfaces within the paradigm of self-consistent homogenization. The local grain constitutive laws are consistent with the description of an interphase layer comprised of local pore volume between grains, such that inelastic inter-particle displacements are directly relatable to changes in bulk porosity, i.e., dilation. The model was developed for the purpose of modeling thermally induced plasticity—the phenomenon known as thermal ratcheting or “ratchet growth”—of composites made from the high explosive triaminotrinitrobenzene (TATB). Model simulations are compared to ratchet growth measurements during cyclic thermal loading of a TATB pellet under stress-free conditions.

Modeling ratchet growth as porosity creep

Modeling ratchet growth as porosity creep

Model for ratchet growth in PBX 9502

Polycrystalline solids composed of crystals with anisotropic thermal expansion coefficients exhibit ratchet growth (RG), a phenomenon characterized by a cumulative and irreversible volume expansion that develops upon exposing the material to cyclic excursions in temperature. We developed a statistical model for RG. The model attributes RG to the formation of intergranular cracks caused by tessellated internal stresses that develop during the thermal excursions. It is postulated that different sets of internal cracks form upon heating and cooling the polycrystalline solid. The model reproduces RG measurements in pressed TATB and PBX 9502 energetic materials and suggests an explanation for why the amplitude of RG generated by a heating excursion is larger than that generated by a subsequent cooling excursion of the same amplitude.

Thermal Cycling and Ratchet Growth of TATB and PBX 9502

AbstractThe irreversible volume expansion, or ratchet growth, of TATB and PBX 9502 (95 weight% TATB) compactions has been quantified over a wide range of thermal cycles. While the precise TATB texture distributions of these specimen sets are likely different from each other, we believe they are consistent within each set, as the expansion data show reproducibility and consistency. These data provide a baseline characterization of the ratchet growth phenomenon in these materials. The increased expansion that comes with changes in the temperature range of the cycles is quantified, repeated hot cycles growing far more than cold. For thermal cycles above ambient where the temperature range is increased in subsequent cycles, the growth of a given cycle is shown to be dictated by previously‐established growth trajectories, and the specimen will grow according to the growth potential associated with the temperature range of the present cycle. Alternating hot‐cold cycles greatly enhances the cold‐cycle contributions as compared to the growth of cold cycles alone. These “rules” of ratchet growth are first established, then observed to hold true for more complex sequences of hot and cold cycles. A simple equation is used to parameterize the response of individual data sets.

Neutron Diffraction Measurements and Micromechanical Modelling of Temperature‐Dependent Variations in TATB Lattice Parameters

AbstractTriaminotrinitrobenzene (TATB) is a highly anisotropic molecular crystal used in several plastic‐bonded explosive (PBX) formulations. TATB‐based explosives exhibit irreversible volume expansion (“ratchet growth”) when thermally cycled. A theoretical understanding of the relationship between anisotropy of the crystal, crystal orientation distribution (texture) of polycrystalline aggregates, and the intergranular interactions leading to this irreversible growth is necessary to accurately develop physics‐based predictive models for TATB‐based PBXs under various thermal environments. In this work, TATB lattice parameters were measured using neutron diffraction during thermal cycling of loose powder and a pressed pellet. The measured lattice parameters help clarify conflicting reports in the literature as these new results are more consistent with one set of previous results than another. The lattice parameters of pressed TATB were also measured as a function of temperature, showing some differences from the powder. This data is used along with anisotropic single‐crystal stiffness moduli reported in the literature to model the nominal stresses associated with intergranular constraints during thermal expansion. The texture of both specimens were characterized and the pressed pellet exhibits preferential orientation of (001) poles along the pressing direction, whereas no preferred orientation was found for the loose powder. Finally, thermal strains for single‐crystal TATB computed from lattice parameter data for the powder is input to a self‐consistent micromechanical model, which predicts the lattice parameters of the constrained TATB crystals within the pellet. The agreement of these model results with the diffraction data obtained from the pellet is discussed along with future directions of research.

Time‐Evolution of TATB‐Based Irreversible Thermal Expansion (Ratchet Growth)

AbstractTATB is an insensitive high explosive, attractive for use because of its safety aspects. TATB compactions, with or without binder, undergo irreversible volume expansion (or ratchet growth) upon thermal cycling. In the past, experimental elucidation of this phenomenon has focused on irreversible expansion as a function of the number of thermal excursions over a given temperature range, where growth is asymptotic with increasing cycle number. In this paper, we demonstrate that ratchet growth also occurs as a function of time at constant temperature, and that growth is substantial at elevated temperatures. We have measured strain response in PBX 9502, a TATB‐based composite, by performing thermal‐cycling tests with different durations at high temperature. Irreversible growth arises from the thermal ramps themselves (increasing and decreasing), as well as from the subsequent isotherms. PBX 9502 specimens with previously‐identified TATB texture/orientation were used in order to eliminate and/or evaluate texture as a variable. Measurements were also performed on dry‐pressed TATB (no binder) to confirm that expansion as a function of time (constant temperature) is not caused by the binder. A simple analysis of the time‐response data demonstrates consistency in the results. We propose that the primary driving force for irreversible expansion is the proximity of the current strain value (due to thermal history) to the strain saturation point of the current cycle (i.e. strain at infinite high‐temperature hold times or an infinite number of cycles). Such tests should aid in the understanding and modeling of ratchet growth response in these materials.

Numerical modeling of the thermal expansion of an energetic material

The thermoelastic response of a TATB-based pressed explosive is studied using morphological modeling and a numerical Fourier scheme. First, we characterize the polycrystalline-like microstructure in terms of the (2D) granulometry and covariance functions, measured on SEM micrograph images. The granulometry is found to be close to a Rayleigh distribution. Second, we represent the polycrystal by a modified Johnson–Mehl tessellation with time-varying germination-rate, in order to approach the wide size distribution observed on the SEM images. We find excellent agreement between the numerically optimized model and the real material in terms of granulometry. Third, we compute the thermoelastic response of the microstructure model by means of full-field Fourier-based computations. Each crystal is assigned uncorrelated random orientations. The thermomechanical response of single crystals is provided by the molecular dynamic simulations of Bedrov et al. (2009) and the X-ray diffraction results of Kolb et al. (1979). Macroscopic (uniform) temperature or strain loadings are applied along various directions (tension, shear or hydrostatic). We observe strong internal stresses upon heating, owing to the highly anisotropic thermoelastic response of TATB and random crystallographic orientations in the polycrystal. The largest stress and strain gradients are observed at grain boundaries, enforcing the idea that grain boundary fracture is indeed the irreversible mechanism underlying ratchet growth. As a first attempt to account for the plastic binder, a 4-voxels soft interphase is inserted at grain boundaries. This results in a strong softening effect on elastic macroscopic properties.

The Effects of TATB Ratchet Growth on PBX 9502

AbstractPBX 9502 is a plastic‐bonded explosive that contains 95 wt.‐% TATB, a graphitic‐structured high explosive known to undergo “ratchet growth,” i.e., irreversible volume change that accompanies temperature excursions. Earlier studies have reported changes in TATB‐based composites as a function of thermal cycling and density change, however, a clear distinction between density and ratchet‐growth effects has not been made. In the work reported here, an “as‐pressed density” baseline for the mechanical response of recycled PBX 9502 is established over a density range of interest, then high‐density specimens are thermally cycled between −55 and 80 °C to achieve “ratchet‐grown” parts in the same low‐density region. As‐pressed and ratchet‐grown specimens with identical densities are then analyzed using microX‐ray computed tomography and USANS techniques to obtain information about pore‐size distributions. Data show that after ratchet‐growth, PBX 9502 specimens contain, in general, more numerous and smaller voids than specimens that were pressed with lower compaction pressures to match the same density. The mechanical response of the ratchet‐grown material is consistent with damage, showing lower tensile stress and modulus, lower compressive modulus, and higher tensile and compressive strain, than as‐pressed specimens of the same density.

The Microstructure of TATB‐Based Explosive Formulations During Temperature Cycling Using Ultra‐Small‐Angle X‐Ray Scattering

AbstractTATB (1,3,5 triamino‐2,4,6‐trinitrobenzene), an extremely insensitive explosive, is used both in polymer‐bound explosives (PBXs) and as an ultra‐fine pressed powder (UFTATB). Many TATB‐based explosives, including LX‐17, a mixture of TATB and Kel‐F 800 binder, experience an irreversible expansion with temperature cycling known as ratchet growth. Additional voids, with sizes hundreds of nanometers to a few micrometers, account for much of the volume expansion. Measuring these voids is important feedback for hot‐spot theory and for determining the relationship between void size distributions and detonation properties. Also, understanding mechanisms for ratchet growth allows future choice of explosive/binder mixtures to minimize these types of changes, further extending PBX shelf life. This paper presents the void size distributions of LX‐17, UFTATB, and PBXs using commercially available Cytop M, Cytop A, and Hyflon AD60 binders during temperature cycling between −55 and 70 °C. These void size distributions are derived from ultra‐small‐angle X‐ray scattering (USAXS), a technique sensitive to structures from about 2 nm to about 2 μm. Structures with these sizes do not appreciably change in UFTATB. Compared to TATB/Kel‐F 800, Cytop M and Cytop A show relatively small increases in void volume from 0.9 to 1.3% and 0.6 to 1.1%, respectively, while Hyflon fails to prevent irreversible volume expansion (1.2–4.6%). Computational mesoscale models combined with experimental results indicate both high glass transition temperature as well as TATB binder adhesion and wetting are important to minimize ratchet growth.