High Strain Rate Material Behaviour


Introduction


Currently, the need to improve automobile efficiency through weight reduction is apparent and one method in which this can be realized by manufacturing conventional automobile structural components with new and lightweight sheet metals. But, in order to accurately model a vehicle crash event using finite elements, the mechanical properties at elevated strain rates are required. This research consists of determining the constitutive behaviour of these new and lightweight metals at high rates of deformation. For each metal, the compiled data consists of flow stress as a function of strain, strain rate, and temperature. Of equal importance is fracture behaviour and damage development under high rates of deformation.

In order to evaluate a materials response throughout the strain rates present during crash, tension tests are conducted at strain rates that range from:

  • High Strain Rate: 500-1500s-¹ tested using a Tensile Split Hopkinson Bar Apparatus (Compressive Split Hopkinson Bar Apparatus is also available)
  • Intermediate Strain Rate: 1.0-100s-¹ using the Hydraulic Intermediate Strain Rate (HISR) apparatus
  • Intermediate Strain Rate: 10-200s-¹ tested using an Instrumented Falling Weight Impactor, otherwise known as a Drop Tower (decommissioned January 2011)
  • Quasi-Static Strain Rate: 0.001-1.0s-¹ tested in a Instron uniaxial tension test apparatus

The alloys that have been tested at the University of Waterloo include:

  • Dual Phase Steel (DP600, DP800, DP980, flat and tube stock)
  • Transformation Induced Plasticity Steels (TRIP780, flat and tube stock)
  • High Strength Low Alloy Steel (HSLA350, flat and tube stock)
  • Drawing Quality Steel (DDQ, DQAK, flat and tube stock)
  • Hot Stamped Boron Steel (100% martensitic and various ratios of martensite/bainite)
  • Magnesium (AZ31B sheet and cast AM60, at various tempers)
  • Aluminum (AA5754, AA5182, AA6111, flat and tube stock)
  • Polymeric (various types including fibre reinforced)

Quasi-Static Strain Rate - Instron Uniaxial Tension Test Apparatus


The quasi-static experiments conducted at the University of Waterloo use an Instron model 1331 servo-hydraulic uniaxial testing machine. The load cell used on this unit has a capacity of 25kN. Specimen displacement was measured using a ±5mm extensometer manufactured by Instron. The specimens were mounted in a pair of custom grips as shown below with the extensometer. The grips are positioned as to align the specimen concentrically with respect to the loading axis of the machine, which reduces the likelihood that bending loads will be applied to the specimen.


Instron Uniaxial Tension Test Apparatus

 

Intermediate Strain Rate - Hydraulic Intermediate Strain Rate (HISR) Apparatus


The hydraulic intermediate strain rate (HISR) apparatus was recently developed at the University of Waterloo.  The apparatus has a 13.3kN (3,000lbf) hydraulic actuator with 101.6mm (4”) stroke.  The apparatus functions by accelerating the engagement sleeve to a constant velocity which then contacts the engagement piston at the bottom of the stroke as shown in the schematic below.  A MOOG high performance servo-valve with a 15GPM capacity is used to achieve a maximum stroke rate of 1500mm/s.  A KISTLER 9500A4 ±30kN piezoelectric load cell, which is located directly above the upper grip assembly, measures the load during the test while the enhanced laser displacement system (ELDS) is used to measure the displacement. The ELDS system is composed of a laser which emits a diverging sheet of light that is then collimated by a plano-cylindrical lens and fixed to a 25.4 mm width by a rectangular aperture. A convex lens is used to focus the laser sheet to a point, where the intensity is measured by a high-speed PIN photodetector. The intensity is converted to a voltage which is recorded by the data acquisition system and converted to displacement upon processing.  Load and displacement are acquired within the HISR system using a National Instruments 6212 USB data acquisition module within a desktop computer with a maximum sampling rate of 250,000 samples per second.

 

HISR apparatus at the University of Waterloo with a schematic showing the ELDS system

HISR
HISR

 

Intermediate Strain Rate - Instrumented Falling Weight Impactor (Drop Tower)


Prior to the development of the HISR, intermediate strain rate tensile testing was conducted using an instrumented falling weight impactor (IFWI) which is also know as a drop tower. A photograph and schematic of the IFWI apparatus at the University of Waterloo are shown below. The specimen is attached to a fixed upper grip and then loaded in tension when the striker (which is free falling) contacts the lower grip. A KISTLER 9500A4 ±30 kN piezoelectric load cell which is located directly above the upper grip measures the load during the test while an enhanced laser displacement system (ELDS) is used to measure the displacement as shown in the figure. Load and displacement are acquired at a rate of 20,000 samples per second.


IFWI apparatus at the University of Waterloo with a schematic showing the ELDS system

High Strain Rate - Tensile Split Hopkinson Bar Apparatus


The tensile split Hopkinson bar (TSHB) apparatus is used to conduct high strain rate tensile tests on sheet metal specimens (can be used to pull cylindrical specimens as well) and the TSHB apparatus at the University of Waterloo is shown in the figure below along with a schematic representation. In this test, a gas gun propels a hollow striker towards the end cap. The impact creates a tensile load on the incident bar which sends a tensile wave along the incident bar towards the specimen. When the tensile wave reaches the specimen, part of the wave is transmitted through the specimen and the remainder is reflected as a compressive wave as shown in the wave data below. Using the Kolsky equations, the stress, strain and strain rate can be calculated using the data. The TSHB at the University of Waterloo has momentum trapping capability, which traps propagating stress waves, thereby allowing interrupted tests to be conducted. Also, a radiative furnace is available to conducted elevated temperature tests that are used to characterize thermal softening.


TSHB apparatus (and schematic) at the University of Waterloo

Typical waveform strain data

Material Characterization


The typical material characterization procedure involves testing a sheetmetal at various strain rates (with the equipment described above) as shown by the flow stress curves below. The experimental data is then typically fit with a constitutive model (Zerilli-Armstrong, Johnson-Cook, modified Voce, etc.) using non-linear regression as shown for room temperature tests and the Zerilli-Armstrong constitutive model. The constitutive model is then used as input for finite element models of vehicle crash.


Effect of strain rate on the flow stress of magnesium. Exp. data (solid lines) and Zerilli-Armstrong constitutive model (dashed lines)

Effect of temperature on the flow stress of magnesium. Exp. data (solid lines) and Zerilli-Armstrong constitutive model (dashed lines)

Finite Element Modeling


LS-DYNA is used to conduct finite element modeling of the high strain rate tensile tests. The various constitutive models determined from the experimental results will be applied to within a user-prescribed material model or umat. Comparisons between experimental results and those predicted by the finite element model will be made to assess the constitutive models as shown below. Damage development will be predicted using a Gurson-based constitutive model.


Finite Element Model of 1000s-¹ test showing contours of true stress


Contacts


Alexander Bardelcik, PhD
abardelc@uwaterloo.ca


Michael Worswick, Professor
worswick@lagavulin.uwaterloo.ca

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