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Review Articles

# Hopkinson Bar Loaded Fracture Experimental Technique: A Critical Review of Dynamic Fracture Toughness Tests

[+] Author and Article Information
Fengchun Jiang

Department of NanoEngineering, University of California, San Diego, La Jolla, CA 92093-0448

Kenneth S. Vecchio

Department of NanoEngineering, University of California, San Diego, La Jolla, CA 92093-0448kvecchio@ucsd.edu

Appl. Mech. Rev 62(6), 060802 (Aug 05, 2009) (39 pages) doi:10.1115/1.3124647 History: Received September 08, 2008; Revised March 10, 2009; Published August 05, 2009

## Abstract

Hopkinson bar experimental techniques have been extensively employed to investigate the mechanical response and fracture behavior of engineering materials under high rate loading. Among these applications, the study of the dynamic fracture behavior of materials at stress-wave loading conditions (corresponding stress-intensity factor rate $∼106 MPam/s$) has been an active research area in recent years. Various Hopkinson bar loading configurations and corresponding experimental methods have been proposed to date for measuring dynamic fracture toughness and investigating fracture mechanisms of engineering materials. In this paper, advances in Hopkinson bar loaded dynamic fracture techniques over the past 30 years, focused on dynamic fracture toughness measurement, are presented. Various aspects of Hopkinson bar fracture testing are reviewed, including (a) the analysis of advantages and disadvantages of loading systems and sample configurations; (b) a discussion of operating principles for determining dynamic load and sample displacement in different loading configurations; (c) a comparison of various methods used for determining dynamic fracture parameters (load, displacement, fracture time, and fracture toughness), such as theoretical formula, optical gauges, and strain gauges; and (d) an update of modeling and simulation of loading configurations. Fundamental issues associated with stress-wave loading, such as stress-wave propagation along the elastic bars and in the sample, stress-state equilibrium validation, incident pulse-shaping effect, and the “loss-of-contact” phenomenon are also addressed in this review.

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## Figures

Figure 1

Configuration of a long NRT bar fracture test developed by Costin (27), in which a NRT sample was loaded to fracture by a direct tensile stress pulse. The displacement was measured by an optical method, Moiré fringes, and the dynamic stress-intensity factor was determined by the quasistatic fracture theory. Reproduced from American Science for Testing Materials, 1977.

Figure 2

Configuration of a reflected tensile fracture test developed by Stroppe (57). A cracked sample was loaded to failure by a tensile stress pulse reflected from a compressive stress pulse at the free end of the sample. Reproduced from “Dynamic fracture of steel at short loading times, impact loading and dynamic behavior of materials.”

Figure 3

Configuration of WLCT fracture test developed by Klepaczko (68). A compact tension specimen is sandwiched in between the loading wedge and the transmission bar and loaded to failure by a compressive stress pulse. Crack initiation time is detected by the small strain gauge mounted near the crack tip and the stress-intensity factor is computed by quasistatic fracture mechanics theory. Reproduced from Klepaczko (68).

Figure 4

Configuration of one-bar/1PB fracture test Mode I fracture toughness measurement developed by Homma (94). A striker bar impacts the incident bar against the 1PB specimen, and generates a compressive stress pulse down the incident bar toward the specimen, which is loaded and fractured by inertial force. Crack initiation time can be detected by the strain gauge and fracture gauge. The dynamic stress-intensity factor can be determined by the FEA and theoretical formulas. Reproduced from Weisbrod and Rittel (98).

Figure 5

Configuration of a one-bar impact test for Mode II fracture toughness measurement developed by Rittel. The cracked side of the sample is in contact with the incident bar, and the sample is loaded to failure in a shear mode. Reproduced from Rittel (25).

Figure 6

Configuration of a one-bar/3PB fracture test for fracture toughness measurement developed by Mines and Ruiz (125). The uncracked side of the sample is in contact with the incident bar. Reproduced from Rubio (137).

Figure 7

Configuration of a two-bar/3PB fracture test for fracture toughness measurement developed by Tanaka (157). A transmission tube acts as the support, and load and displacement are determined by the transmitted and reflected pulses, respectively, under stress-equilibrium conditions. Reproduced from Tanaka and Kagatsume (158).

Figure 8

Configuration of a modified two-bar/3PB fracture test for fracture toughness measurement developed by Vecchio’s group at UCSD. Pulse-shaping and momentum-trapping techniques are adopted for achieving a tailored loading pulse (171).

Figure 9

Loading configuration of a three-bar/3PB fracture test developed by Yokoyama. Here one incident bar serves as an impactor and two transmission bars act as supports. The dynamic stress-intensity factor is computed by FEA using both incident and transmitted loads; the one-point strain measurement method was applied. Reproduced from Yokoyama and Kishida (181).

Figure 10

Configuration of a two-bar/CCS fracture test for fracture toughness measurement developed by Rittel A compact compression sample is sandwiched between the incident and transmission bars, and crack initiation time is detected by a fracture gauge. Reproduced from Rittel (203).

Figure 11

Configuration of a two-bar/Brazilian disk fracture test for brittle materials. A Brazilian disk sample with a center notch is sandwiched between the incident and transmission bars and loaded to failure by a compressive pulse. The Mode I and Mixed Mode I/II fracture tests can be performed by changing the angle θ. Reproduced from Zhou (227).

Figure 12

Crack-tip coordinate reference 298

Figure 13

The comparison of natural frequency ω1/ω0 determined by different models. Here the frequencies are normalized by the fundamental frequency of a simply supported uncracked beam, i.e., ω0=(π/S)2EI/ρA. The specimen dimensions are 10×10×55 mm3 with a/W=0.5, S/W=4, and it is assumed to be in a state of plane strain (169).

Figure 14

Typical signals from strain gauges and fracture gauges for fracture time measurement: (a) recorded by a small strain gauge attached near the crack tip. Here a strain gauge with gauge dimensions of 0.79×1.57 mm2 was affixed at 1.5 mm from the crack tip, a high-strength steel sample (6.5 mm(width)×4 mm(thickness)×40 mm(length)) with relative crack length of a/W=0.5 was loaded to failure in a Hopkinson bar four-point bend fracture test; (b) recorded by a fracture gauge mounted ahead of the crack tip. Here a single wire fracture gauge, and a tungsten base heavy alloy Charpy type sample (10 mm(width)×8 mm(thickness)×23 mm(length)) with a relative crack length of a/W=0.4 were used. (b) is reprinted from Weisbrod and Rittel (98).

Figure 15

A selected sequence of high-speed images shows the contact situation between the impactor and specimen (small steel specimen) during the loading process in the current setup. Time origin is taken when the stress wave reaches uncracked surface of the specimen. Photos (a)–(h) show time sequences for a singular, representative experiment. A crack initiation is visible in image (c) (171).

Figure 16

Comparison between the measured and predicted load and displacement: (a) The variation of load as a function of time, and (b) the variation of displacement as a function of time. Case (A): the effect of plastic deformation in the contact zone on the contact stiffness is neglected in consideration of the effect of crack propagation on the sample’s stiffness; Case (B) the effect of plastic deformation in the contact zone on the contact stiffness is neglected, and the effect of crack propagation on the sample’s stiffness is neglected; Case (C) the effect of crack propagation and plastic deformation in the contact zone on sample deflection is included; and Case (D) the effect of crack propagation on sample deflection is included, and the effect of plastic deformation in the contact zone is neglected (170).

Figure 17

Typical stress pulses (incident, reflected, and transmitted) obtained from small un-notched high-strength steel specimens under two-bar/4PB loading. (a) Without a pulse shaper; (b) with a pulse shaper; (an aluminum sheet pulse shaper with dimensions of ∼240 mm2×0.5 mm (thickness) is used). The rise time and duration of the incident pulse, time parameter Δt, and time interval are all altered by pulse-shaping (174).

Figure 18

Typical output voltage variations as a function of time obtained from a high-strength sample: (a) smaller sample, 4 mm(thickness)×6.5 mm(width)×40 mm(length), and (b) larger sample, 4 mm(thickness)×10 mm(width)×40 mm(length). Time origin is taken when the incident pulse begins traveling in the incident bar. Here, the relative crack lengths are both a/W∼0.5(171).

Figure 19

Typical dynamic load (PI and PII) comparison for un-notched high-strength steel specimens. The loads were computed using Eqs. 8,9. (a) Without a pulse shaper; and (b) with a pulse shaper (1-ply paper towel pulse shaper). Times required for stress-state equilibrium are ∼50 μs and ∼16 μs under unshaped-pulse and pulse-shaped tests, respectively, indicating that the time for stress-equilibrium state is reduced by pulse-shaping (174).

Figure 20

Typical dynamic loads (PI and PII) comparison for small notched and cracked high-strength steel specimens; the loads were computed by Eqs. 8,9. (a) Notched, untempered sample; and (b) precracked, tempered sample. Here, the relative crack lengths are both a/W∼0.5, and a 1-ply paper towel pulse shaper was used. The times for stress-equilibrium are ∼19 μs and ∼23 μs for the notched and precracked specimens, respectively, indicating the time for stress-equilibrium is slightly larger in cracked specimen (174).

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