Abstract

Uniaxial tension tests were conducted on ASTM A572-50 and A992 steel at increasing strain rates to determine material strength properties of structural members subjected to dynamic loadings. The increase in dynamic yield strength and ultimate tensile strength, defined as the dynamic increase factor (DIF), versus strain rate was determined to provide the necessary information to efficiently design blast resistant structures utilizing modern day structural steel. Dynamic strength properties were determined by high-rate tensile tests using a hydraulic testing apparatus and compared to static values obtained from ASTM E8 standard tension tests. The comparisons were used to calculate the DIF of each steel at strain rates ranging from 0.002 to 2.0 inch/inch/second. Experiments revealed that A572-50 steel exhibited an increase in yield strength up to 35% and ultimate tensile strength up to 20% as strain rate increased over the range tested. A992 steel exhibited a similar increase in yield strength up to 45% and ultimate tensile strength up to 20%. DIF versus strain rate curves obtained during this research will be used to develop criteria within the structural steel design chapter of Unified Facilities Criteria (UFC) 3-340-02 (2014) for A572-50 and A992 steel.

Truncated presentation of "Effects of High Strain Rates on ASTM A992 and A572 Grade 50 Steel" [1].

"High" strain rate classification applies to shock-induced blast loading community. Actual strain classification is ~intermediate strain rate.

Test Methods

Test Specimen

ASTM A572-50 specimens were fabricated from a domestic, nominal 0.375-in.-thick plate. The mill test report (MTR) indicated that the plate also met the specifications of ASTM A709-50. ASTM A992 specimens were obtained from the web of domestic S12x31.8 beams, which had a nominal thickness of 0.35 in. The MTR for the A992 steel indicated the beam also met specifications of ASTM A6, A709-50, A572-50, and A36. The chemical composition (weight percent) of the tested materials is listed in the table below, as specified by the MTRs.

Static-rate specimen were waterjet cut to ASTM E8 standard sheet-type geometries. Dynamic-rate specimens were waterjet cut into a modified pin-type specimen geometry shown in Figure 1 with tolerances similar to those in ASTM E8. The full thickness of the parent material was used. Bolt holes were drilled using a computer numerical control (CNC) machine. Figure 2 provides a visual comparison of the static and dynamic specimens.

Equipment

The U.S. Army Engineer Research and Development Center's (ERDC) Instron 33R4206 Universal Testing System (Figure 3) was used to conduct the static, uniaxial tension tests. An integrated optical extensometer was used to record elongation over time. The apparatus allowed controlled-rate testing at an average elastic strain rate of approximately 0.00002 s^-1.

Dynamic Tension Test Apparatus

ERDC’s 200-kip-capacity hydraulic loader (Figure 4) was used to conduct the dynamic, uniaxial tension tests. This loader has been employed by ERDC to conduct dynamic experimentation on reinforcing steel, splices, and fasteners since the 1970’s, and it remains the approved validation apparatus for the dynamic testing of mechanical splices for reinforcing steel used in protective design.

The device was slowly pressurized by pumping compressible silicon oil into the top and bottom pressure chambers. Pressure in the top chamber was kept at a slightly higher pressure in order to maintain a small tensile preload (50-1,000 lbf) on the specimen. The measured preload ensured alignment of the specimen through the bolted connections and also seated the top reaction stem pivot joint to further ensure axial loading of the specimen. Once the desired fluid pressure was reached, a quick-opening valve leading to an empty expansion tank was opened. Pressure in the lower chamber was rapidly reduced allowing the piston to translate downward and apply a tension load to the specimen attached above. Flow rate of the fluid in the lower chamber into the expansion tank was controlled by an adjustable orifice and was the main variable in changing the loading rate (strain rate) applied to the test specimen.

The adjustable orifice allows for specimen strain rates of approximately 0.001 to 4.0 s^-1, and the limits are dependent on specimen geometry, specimen stiffness, and oil pressure. The lowest strain rate recorded during experimentation was 0.002 s^-1 with the smallest obtainable orifice setting, and the highest was 2.91 s-1 with the largest orifice setting. The UFC lists strain rates for bending, tension, and compression modes at various pressure levels. Provided strain rates range from 0.02 to 0.30 s^-1, and were well within the strain rate limits of the hydraulic loader.

Instrumentation

Strain

Axial deformation was measured using a Phantom Miro 320S high-speed (HS) camera. The HS camera recorded locations of gauge marks from time zero (trigger) through fracture of the specimen. The video was uploaded into Image System’s TrackEye Motion Analysis (TEMA) software, which incorporated an optical extensometer feature that tracked each gauge mark location, represented by a single pixel, frame by frame throughout the length of the video recording. The software then output the distance between gauge marks (elongation) with respect to time as they moved from pixel to pixel. Quadrant markers were added to the specimen to enhance the tracking capabilities of the TEMA software. Pixel length was determined by the vertical resolution of the HS camera recording and the distance between the tracked points. The vertical resolution was set to the maximum of 1,200 pixels, which provided an elongation measurement accurate to approximately 0.00105 in., or 185 microns of strain, for the rates of 0.002 to 0.05 s^-1. At higher strain rates, the collection rate was increased, forcing the vertical resolution to be reduced to 904 pixels, which allowed an approximate accuracy of 0.00155 in. for elongation and 255 microns for strain. The HS camera software was calibrated to remove error due to lens distortion using the prescribed TEMA lens calibration guidelines.

Even with a collection rate of 13,000 frames per second, for experiments conducted at the highest rate (≈ 2.0 s^-1) the HS camera was only able to obtain roughly 20 data points before the specimens would yield. Bonded strain gauges were implemented at this rate to obtain high resolution strain data up to yield to supplement the HS Camera data. Strain gauges were applied to specimens used for strain rate calibration and specimens tested at 2.0 s^-1. For these specimens, it was necessary to remove mill scale from the parent material to facilitate strain gauge bonding. Approximately 0.006 in. (< 2% of thickness) of material was removed by machining across the entire gauge region, which allowed application of a strain gauge to the exposed steel at the center of the gauge region. A schematic of the test assembly showing the dynamic specimen and locations of instrumentation is shown in Figure 5.

Load

Load was measured using two load cells in series with the 200-kip-loader tension ram. The load cells were fabricated from AISI 4130 quenched and tempered steel with a minimum yield strength of 100 ksi. The bridge network used on the load cells consisted of eight strain gauges installed in pairs at the quarter points, midway in the necked down portion of the load cell. One gauge of each pair measured axial strain and the other measured Poisson’s effect. The active gauges were on the opposite sides of the bridge topology with the adjacent Poisson gauges electrically connected on opposite sides as well. Calibration of the load cells was conducted by placing both in series with a pre-calibrated, manufactured load cell. The load cells were statically calibrated to a maximum load of 200 kip. Post-test verification indicated that the load cells maintained calibration throughout all dynamic experiments.

Acceleration

Two accelerometers (Meggit, model 7280A) were used to record acceleration during experiments conducted at rates of 0.05 s^-1 and higher. Data recorded from these devices allowed inertial load effects to be determined and removed from the load versus time history. Accelerometers were mounted in an orientation that measured positive acceleration in the upward direction.

Load Analysis and Data Reduction

Inertial Force Correction

Newton’s second law explains that when force is applied to objects with mass, inertial forces develop to resist the impending motion. If the objects have a large mass or if the accelerations are high, these inertial forces become quite significant. When the tension ram of the testing machine began to first apply rapid load onto the specimen through the lower grip, the mass of the grip and specimen resisted the downward acceleration. Increased load was required to overcome this inertial resistance and begin pulling the lower grip and half of the specimen downward applying tension. The lower load cell recorded, as one total load, both the applied load to the specimen and the load required to overcome inertia. Inertial force was subtracted from the bottom load cell record to form a corrected load applied to the specimen. Contrarily, addition of inertial force was required for the top load cell record to form the corrected load applied to the specimen. An uncoupled (mass) spring-mass model (Figure 6) was used to develop the required load correction equations. Equilibrium equations (Eq. 1-3) were developed to solve for the corrected load applied to the specimen.

where:
F(t) = applied force as function of time (lbf)
M₁ = mass of top specimen grip and half of the test specimen (lbm)
M₂ = mass of bottom specimen grip and half of test specimen (lbm)
M₃ = mass of tension ram and piston (lbm)
a₁ = acceleration of M₁ (g)
a₂ = acceleration of M₂ (g)
a₃ = acceleration of M₃ (g)
k₁ = spring constant of upper reaction member (lbf/in.)
k₂ = spring constant of test specimen (lbf/in.)
k₃ = spring constant of tension ram and piston (lbf/in.)
x₁ = displacement of M₁ (in.)
x₂ = displacement of M₂ (in.)
x₃ = displacement of M₃ (in.)

Eq. 1 represents the corrected load on the specimen using the top load cell and acceleration data. Eq. 2 was solved to determine the corrected load using the bottom load cell and acceleration data (Eq. 4).

Since the accelerometers were mounted in an orientation that recorded positive acceleration in the upward direction, accelerations in Eq. 1 and Eq. 4 were corrected by switching the signs of a₁ and a₂ to form Eq. 5 and Eq. 6, respectively. Substitution allows for Eq. 7 to be derived, which states that the corrected load using the top data records, load and acceleration, should theoretically be equal to the corrected load using the bottom data records. Testing at the static rate (0.00002 s^-1) and the dynamic rate of 0.002 s^-1 produced accelerations of insignificant magnitudes and were therefore neglected.

Figures 7-8a shows an example inertial force correction for both the top and bottom load cell data for the highest strain rate experiments (≈ 2.0 s^-1). The bottom load cell, attached to the tension ram of the loader, experiences up to four times the acceleration of the upper; therefore, the inertial load correction is much more significant on the bottom load cell data. The average of the corrected top and corrected bottom load versus time histories are used for the calculation of engineering stress.

Data Analysis

The average corrected load was divided by the original cross section of the test specimen to calculate engineering stress. Average strain was determined from elongation data. Stress was plotted as a function of strain to develop the stress-strain diagram for each test. Upper yield strength was determined as the stress corresponding to the maximum force at the onset of discontinuous yielding as prescribed in ASTM E8-7.7.3. Ultimate tensile strength was calculated by dividing the maximum force applied to the specimen during the test by the original cross-sectional area of the specimen (E8-7.10). The strength properties were rounded to the nearest 0.1 ksi. Strain rate was determined by calculating the slope of the strain-time data in the elastic deformation region.

The ratio of dynamic-to-static yield stress is defined as the dynamic increase factor (DIFy) at a specified strain rate. The tested A572-50 and A992 steels both exhibited discontinuous yielding. ASTM specifies minimum yield stress values for these steels based on the yield point; therefore, the yield point (upper yield strength) was used in determining DIFy using Eq. 8. Figure 8b indicates the values used in the equations below on a static and dynamic stress-strain diagram.

where:
DIF_y = dynamic increase factor for yield strength for a particular strain-rate
DIF_u = dynamic increase factor for ultimate tensile strength for a particular strain rate
ƒ_dy = dynamic yield strength at a particular strain rate above static (ksi)
ƒ_du = dynamic ultimate tensile strength at a particular strain rate above static (ksi)
ƒ_y = average yield strength measured during static testing (ksi)
ƒ_u = average ultimate tensile strength measured during static testing (ksi)

Results

Eight static-rate tension tests were originally conducted for each steel. Six more were required to verify the static properties of a surplus A992 beam that was obtained to fabricate additional specimens required to complete the dynamic experiments. A minimum of five dynamic-rate tension tests were conducted at each rate. In some cases additional dynamic tests were conducted to compensate for specimens that fractured on gauge marks. A comparison of load histories between specimens that fractured on gauge marks and those that did not indicated no identifiable impact on yield strength or UTS; therefore, results from these experiments were included in the analysis of DIF data. Ductility properties for the specimen that fractured on gauge marks were uncharacteristically low and were not included in percent elongation or reduction of area analysis.

Table 2 lists the number of tension tests conducted at each target strain rate. The average material strength values and standard deviations for each target strain rate are listed in Tables 3-4. The strain rate corresponding to each targeted rate could not be kept constant between tests; however, dynamic yield and UTS values were obtained without a substantial amount of distribution when grouped by target strain rate. Standard deviation for the static yield strength was 0.27 ksi for A572-50 and 1.38 ksi for A992. The static UTS standard deviation was 1.43 ksi for A572-50 and 0.48 ksi for A992. Deviations for the dynamic-rate tests were of a similar order of magnitude as the static.

The measured yield strength and UTS for each experiment are shown in Figure 9. Static yield strength (ƒ_y) and UTS (ƒ_u) were determined by averaging values obtained from static testing of each material. The DIF for yield (DIF_y) and UTS (DIF_u) were calculated with Eq. 8 and Eq. 9, respectively. The calculated values were graphed in DPlot software. Analysis of the data led to formulation of a bi-linear least-squares regression curve fit on a log-linear DIF versus strain rate plot. Individual values for each experiment and curve fits are shown in Figure 10. The percent elongation after fracture and percent reduction of area for each experiment are shown in Figure 11a.

Acknowledgments

This research is the product of the U.S. Army Engineer Research and Development Center, Geotechnical and Structures Laboratory and was funded by the Department of Defense Explosives Safety Board.

References

1. Murray, Matthew P, Stephen P Rowell, and Trace A Thornton. 2018 “Effects of High Strain Rates on ASTM A992 and A572 Grade 50 Steel.” In International Explosives Safety Symposium and Exhibition, 2018. San Diego, CA: NDIA. https://ndiastorage.blob.core.usgovcloudapi.net/ndia/2018/intexpsafety/MurrayPaper.pdf.