Computational Comparisons of Homogeneous and Statistical Descriptions of Steel Subjected to Explosive Loading

2010 ◽  
Author(s):  
Michael V. Hopson ◽  
David E. Lambert ◽  
Joseph Weiderhold
Keyword(s):  
Plane Strain ◽  
Computational Analysis ◽  
Stress Triaxiality ◽  
Uniaxial Stress ◽  
Explosive Loading ◽  
Ring Test ◽  
Tungsten Alloy ◽  
Expansion Velocity ◽  
Water Tank ◽  
Stress States

Experiments were conducted by the Munitions Directorate at the Air Force Research Laboratory to investigate the fracture and fragmentation of two different metals due to explosive loading. The first metal, Eglin Steel 1 (ES-1), was a high strength steel alloy configured as a thin shell surrounding the explosive core. The second metal, Aero 224, was a tungsten alloy configured as a stack of rings around the explosive core. The two different configurations generated two different stress states, plane-strain and uniaxial stress. The radial expansion velocity of the ES-1 shell was recorded via a photonic Doppler velocimeter (PDV). Also, the fragments from the ES-1 shell test and Aero 224 ring test were soft captured in a water tank. Complimentary computational analysis was conducted at the Naval Surface Warfare Center Dahlgren Division. The Eulerian wave propagation code, CTH, was used to analyze the stress states of the different configurations and also investigate the use of statistical compensation on explosive fragmentation. The stress states were examined in the context of stress triaxiality where triaxiality is defined as the ratio of pressure to the Von Mises stress. From the computational analysis both the ES-1 shell test and Aero 224 ring test approached, but did not reach the ideal triaxial values for plane-strain and uniaxial stress. Lastly, parametric calculations were conducted in order to determine the effectiveness of using a statistically compensated Johnson Cook fracture model to simulate the non-homogeneous nature of the ES-1 and Aero 224. While using the model did result in different fragment distributions, all the resulting distributions were less accurate than the baseline homogeneous calculation. Scrutiny of the early time fragment formation in the statistically compensated calculations revealed a mesh bias which caused material failure on surfaces parallel to the Cartesian axes. This preferential fracture produced rarefaction waves which prohibited further fragmentation thus generating fragment distributions larger than those observed in the Aero 224 ring test. Potential solutions for this issue will be explored in the future.

Explosively Driven Fragmentation Experiments for Continuum Damage Modeling

2010 ◽  
Author(s):  
David E. Lambert ◽  
Joseph Weiderhold ◽  
John Osborn ◽  
Michael V. Hopson
Keyword(s):  
Plane Strain ◽  
High Speed ◽  
Stress Triaxiality ◽  
High Strength ◽  
Uniaxial Stress ◽  
Tungsten Alloy ◽  
Design Parameters ◽  
High Speed Photography ◽  
Cylinder Wall ◽  
Data Set

The explosively loaded right-circular tube geometry is used as the basis for dynamic fracture and fragmentation modeling. Details of the cylinder configuration are investigated to prescribe controlled loading conditions of uniaxial stress and plane strain. Earlier works by Goto et al [1] had used thin-walled tubes to provide plane strain loading and shorter “rings” to establish uniaxial stress conditions. This paper extends on that work to look at alternative cylinder dimensions and metals of interest. A tungsten alloy, Aero-224, and a high strength steel, Eglin Steel (ES-1), are the subject metals. Transient continuum-mechanics simulations evaluated whether the stress triaxiality conditions were being met as design parameters of cylinder material, cylinder wall-thickness, cylinder length, and initiation configuration were varied. Design analysis shows that the thin cylinders of ES-1 steel do establish the desired plane strain conditions as it expands to failure. Ultra-high speed photography experiments verify the time of fracture and correlate casewall expansion and velocity measurements. Synchronization of the code and diagnostics measurements is presented as a valuable analysis method. On the other hand, rings (i.e. uniaxial stress) of the Aero-224 tungsten alloy were failing just short of uniaxial stress approximating conditions. Analysis of the Aero-224 rings indicated it must be capable of achieving at least a 25% strain to failure in order to have the triaxiality condition satisfied. Strain to failure measurements directly from recovered fragments were less than 14%. Nevertheless, a Weibull distribution was fit to the empirical data set and used to drive a statistically compensated fracture model. Results and discussion of the failure strain distribution and the ability for continuum codes to adequately conduct such simulations are presented.

Behavior of Lode Dependent Plasticity at Plane Strain Condition and its Implication to Ductile Fracture

2016 ◽  
Vol 258 ◽  
pp. 213-216 ◽  
Author(s):  
František Šebek ◽  
Jindrich Petruška ◽  
Petr Kubík
Keyword(s):  
Ductile Fracture ◽  
Plane Strain ◽  
Uniaxial Stress ◽  
Complex Materials ◽  
Fracture Criteria ◽  
Dependent Plasticity ◽  
Ductile Fracture Criteria ◽  
Stress States ◽  
Aluminum Alloy 2024 ◽  
Von Mises

Variety of metals are complex materials exhibiting various behavior under different loading. Many metallic materials exhibit Tresca-like behavior rather than von Mises. It means different behavior in tension under plane strain and uniaxial stress conditions. This might be described by Lode dependent plasticity which should result in better prediction in force or torque responses of material tests. Good agreement between computation and experiment is also very important when calibrating the ductile fracture criteria. Several tests under plane strain and uniaxial stress states were carried out on aluminum alloy 2024-T351 where the Lode dependency was significant. The Lode dependent plasticity was implemented along with von Mises and Tresca-like yield criteria, which resulted in improvement of force–displacement responses of plane strain tests simulations. But it also caused significant change in the stress state of tensile flat and grooved plates which wrongly approached uniaxial tension condition. This inconvenience prevents plane strain experiments from using for calibration of ductile fracture criteria under these circumstances.

Dynamic Fragmentation Experiments Under Plane Strain and Uniaxial Stress Conditions

2010 ◽  
Author(s):  
David E. Lambert ◽  
Joseph Weiderhold ◽  
John Osborn ◽  
Michael V. Hopson
Keyword(s):  
Plane Strain ◽  
Uniaxial Stress ◽  
Stress Conditions ◽  
Tungsten Alloy ◽  
Design Parameters ◽  
High Speed Photography ◽  
Cylinder Wall ◽  
Loading Conditions ◽  
Dynamic Fragmentation ◽  
Fracture Models

The explosively loaded cylinder is further studied as an experimental method to improve dynamic fracture and fragmentation modeling. Details of the cylinder configuration are investigated to prescribe controlled loading conditions of uniaxial stress and plane strain. Commonly used fracture models, e.g. Johnson-Cook, are calibrated with strain at fracture under such controlled conditions. Earlier works by Goto, et al [1] had used thin-walled tubes to provide plane strain loading and shorter “rings” to establish uniaxial stress conditions. This paper extends on that work to look at alternative cylinder dimensions and metals of interest. A tungsten alloy, Aero 224, and a high strength steel, Eglin Steel (ES-1), are the subject metals. Dynamic, continuum-mechanics based modeling and simulations evaluated whether the stress triaxiality conditions are being met as design parameters of cylinder wall-thickness, explosive type, and initiation configuration. Experiments conducted for this effort, reported in greater detail by Weiderhold [2], provided precise measurement of the cylinder expansion process and fragmentation distributions. An explosively driven metal event is usually considered highly transient and multi-dimensional in stress; however, selective design of the system can result in a controlled experimental configuration. The analysis shows that the ductile ES-1 steel cylinder and rings do establish the desired plane strain and uniaxial stress conditions, respectively, as the cylinder expands to failure. Ultra-high speed photography experiments verify the time of fracture and correlate casewall expansion and velocity measurements. The analysis of the tungsten alloy had verified that if the material was capable of achieving at least a 25% strain to failure then the cylinder and rings would be viable controlled loading paths. However, fragments recovered from the explosively driven rings verified that the strain to failure was less than 14% and the triaxiality condition of uniaxial stress was not achieved by then. The data of this fragmentation under controlled loading conditions are to be used to determine coefficients for fracture-models and serve as benchmarks of relevant, dynamic fragmentation processes for future explosive/metal design opportunities.

scholarly journals Stress Triaxiality and Lode Angle Parameter Characterization of Flat Metal Specimen with Inclined Notch

Metals ◽  
2021 ◽  
Vol 11 (10) ◽  
pp. 1627
Author(s):  
Jian Peng ◽  
Peishuang Zhou ◽  
Ying Wang ◽  
Qiao Dai ◽  
David Knowles ◽  
...  
Keyword(s):  
Stress State ◽  
Notch Root ◽  
Stress Triaxiality ◽  
Image Correlation ◽  
Notch Angle ◽  
Strain Evolution ◽  
Metal Specimen ◽  
Lode Angle ◽  
Stress States ◽  
Angle Parameter

The stress state has an important effect on the deformation and failure of metals. While the stress states of the axisymmetric notched bars specimens are studied in the literature, the studies on the flat metal specimen with inclined notch are very limited and the stress state is not clearly characterized in them. In this paper, digital image correlation and finite element simulations are used to study the distribution of strain and stress state, that is stress triaxiality and Lode angle parameter. Flat specimen with inclined notch was tested to extract the full field strain evolution and calculate stress state parameters at three locations: specimen centre, notch root and failure starting point. It is found that compared with the centre point and the notch root, the failure initiation point can better characterize the influence of the notch angle on the strain evolution. Conversely, the centre point can more clearly characterize the effect of the notch angle on stress state, since the stress states at the failure point and the notch root change greatly during the plastic deformation. Then the calculated stress state parameters of the flat metal specimen with inclined notch at the centre point are used in Wierzbicki stress state diagram to establish a relationship between failure mode and stress state.

Ring Specimen Geometry for Determining the Ductility of Tubulars

2016 ◽  
Author(s):  
M. A. Al Khaled ◽  
I. Barsoum
Keyword(s):  
Stress State ◽  
Plane Strain ◽  
Stress Triaxiality ◽  
Ductile Failure ◽  
Pressure Vessels ◽  
Ring Specimen ◽  
Lode Parameter ◽  
Wide Range ◽  
Failure Locus

Pressure vessels designed in accordance with the ASME BPVC code are protected against local ductile failure. Recent work has shown that local ductile failure highly depends on the stress state characterized by both stress triaxiality (T) and the Lode parameter (L). In this paper, the effect of stress state on the ductility of a tubular steel is studied. Two ring specimen configurations were optimized to allow the determination of the ductile failure locus of both tensile and plane strain loadings. The geometry of both ring specimen configurations was optimized to achieve a plane strain (L = 0) condition and a generalized tension (L = −1) condition. Notches with different radii were machined on both types to achieve a wide range of stress triaxiality. Specimens were manufactured from SA-106 carbon tubular steel and were tested to determine the ductile failure loci as a function of T and L. Failure locus of SA-106 steel was constructed based on the failure instants and was found to be independent of the variation in the Lode parameter. The ASME-BPVC local failure criterion showed close agreement with experimental results.

A Hybrid Experimental-Numerical Test Specimen for Laminated Composite Materials

1991 ◽  
Vol 113 (3) ◽  
pp. 193-196
Author(s):  
W. K. Rule ◽  
G. E. Weeks
Keyword(s):  
Numerical Test ◽  
Cost Savings ◽  
Laminated Composite ◽  
Uniaxial Stress ◽  
Testing Procedure ◽  
Biaxial Stress ◽  
Element Analysis ◽  
Laminated Composite Materials ◽  
Stress States ◽  
A New Technique

A new technique is described for determining all four elastic constants of a lamina from a single laminated specimen of arbitrary, symmetric lay-up. This specimen is subjected to three different loading conditions, and the experimental data is reduced by means of a finite element analysis. The testing procedure for the specimen is relatively easy, which can result in considerable time and cost savings over traditional methods. The new specimen generates biaxial stress states. Thus, the material properties determined from such a configuration may be more appropriate for later use in structural analysis than those determined from traditional specimens with uniform uniaxial stress states.

scholarly journals Strain Rate-Dependent Constitutive and Low Stress Triaxiality Fracture Behavior Investigation of 6005 Al Alloy

2018 ◽  
Vol 2018 ◽  
pp. 1-14 ◽  
Author(s):  
Yong Peng ◽  
Xuanzhen Chen ◽  
Shan Peng ◽  
Chao Chen ◽  
Jiahao Li ◽  
...  
Keyword(s):  
Flow Stress ◽  
Plastic Strain ◽  
Strain Rate ◽  
Fracture Behavior ◽  
Equivalent Plastic Strain ◽  
Stress Triaxiality ◽  
Tensile Tests ◽  
Uniaxial Tensile ◽  
Strain Rates ◽  
Stress States

In order to study the dynamic and fracture behavior of 6005 aluminum alloy at different strain rates and stress states, various tests (tensile tests at different strain rates and tensile shearing tests at five stress states) are conducted by Mechanical Testing and Simulation (MTS) and split-Hopkinson tension bar (SHTB). Numerical simulations based on the finite element method (FEM) are performed with ABAQUS/Standard to obtain the actual stress triaxialities and equivalent plastic strain to fracture. The results of tensile tests for 6005 Al show obvious rate dependence on strain rates. The results obtained from simulations indicate the feature of nonmonotonicity between the strain to fracture and stress triaxiality. The equivalent plastic strain reduces to a minimum value and then increases in the stress triaxiality range from 0.04 to 0.30. A simplified Johnson-Cook (JC) constitutive model is proposed to depict the relationship between the flow stress and strain rate. What is more, the strain-rate factor is modified using a quadratic polynomial regression model, in which it is considered to vary with the strain and strain rates. A fracture criterion is also proposed in a low stress triaxiality range from 0.04 to 0.369. Error analysis for the modified JC model indicates that the model exhibits higher accuracy than the original one in predicting the flow stress at different strain rates. The fractography analysis indicates that the material has a typical ductile fracture mechanism including the shear fracture under pure shear and the dimple fracture under uniaxial tensile.

New Ring Specimen Geometries for Determining the Failure Locus of Tubulars

2017 ◽  
Vol 140 (1) ◽  
Author(s):  
M. A. Al-Khaled ◽  
I. Barsoum
Keyword(s):  
Stress State ◽  
Plane Strain ◽  
Stress Triaxiality ◽  
Ductile Failure ◽  
Pressure Vessels ◽  
Ring Specimen ◽  
Lode Parameter ◽  
Wide Range ◽  
Failure Locus

Pressure vessels designed in accordance with the ASME BPVC code are protected against local ductile failure. Recent work has shown that local ductile failure highly depends on the stress state characterized by both stress triaxiality (T) and the Lode parameter (L). In this paper, the effect of stress state on the ductility of a tubular steel is studied. Two ring specimen configurations were optimized to allow the determination of the ductile failure locus at both tensile and plane strain loadings. The geometry of both ring specimen configurations was optimized to achieve a plane strain (L=0) condition and a generalized tension (L=-1) condition. Notches with different radii were machined on both types to achieve a wide range of stress triaxiality. Specimens were manufactured from SA-106 carbon tubular steel and were tested to determine the ductile failure loci as a function of T and L. Failure locus of SA-106 steel was constructed based on the failure instants and was found to be independent of the Lode parameter. The ASME-BPVC local failure criterion showed close agreement with experimental results (EXP).

Comparison of Notched Bar Creep Behavior of Various Alloys

2010 ◽  
Author(s):  
Yukio Takahashi
Keyword(s):  
Strain Rate ◽  
High Stress ◽  
Stress Triaxiality ◽  
Inelastic Strain ◽  
Creep Rupture ◽  
Creep Tests ◽  
Temperature Parameter ◽  
Stress States ◽  
Proper Consideration ◽  
Rupture Behavior

Possibility of creep rupture needs to be evaluated in design of various components operating at high temperatures. Multiaxial stress states need to be treated in many components and its proper consideration is of critical importance, in addition to the creep rupture behavior under uniaxial tension. In order to examine creep rupture behavior under high stress triaxiality, creep tests were conducted on notched bar specimens of various alloys used in power generation facilities. It was found that all materials showed notch-strengthening behavior but some materials showed considerable reduction of deformation at rupture, in comparison with the plain specimens. Its amount was not similar but strongly dependent on material, being larger in high chromium steels, and smaller in an austenitic stainless steel. It was found that the dependency of true rupture strain on temperature and inelastic strain rate in each material can be successfully modeled by a strain rate-temperature parameter.

Evaluation of a Modified Monotonic Neuber Relation

1991 ◽  
Vol 113 (1) ◽  
pp. 1-8 ◽  
Author(s):  
W. N. Sharpe ◽  
K. C. Wang
Keyword(s):  
Plane Strain ◽  
Notch Root ◽  
Strain Curve ◽  
Uniaxial Stress ◽  
Predictive Capability ◽  
Stress Strain Curve ◽  
Interferometric Technique ◽  
Strain Stress ◽  
Concentration Factors ◽  
Elastoplastic Strains

It has been proposed in the literature that the Neuber relation be modified to read Kε/Kt×(Kσ/Kt)m=1 in order to improve its predictive capability when plane strain loading conditions exist. Kε, Kσ, and Kt are respectively the strain, stress, and elastic concentration factors. The exponent m is proposed to be 1 for plane stress and 0 for plane strain. This paper reports the results of biaxial notch root strain measurements on three sets of double-notched aluminum specimens that have different thicknesses and root radiuses. Elastoplastic strains are measured over gage lengths as short as 150 micrometers with a laser-based in-plane interferometric technique. The measured strains are used to compute Kε directly and Kσ using the uniaxial stress-strain curve. The exponent m can then be determined for each amount of constraint. The amount of constraint is defined as the negative ratio of lateral to longitudinal strain at the notch root and determined from elastic finite element analyses. As this ratio decreases for the three cases, the values of m are found to be 0.65, 0.48, and 0.36. The modified Neuber relation is an improvement, but discrepancies still exist when plastic yielding begins at the notch root.

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