Modeling of stresses, temperature in impacts of elastomeric bumpers

Industrial staple guns and nail drivers use elastomeric bumpers to absorb excess mechanical impact forces. A piston, usually powered by a pneumatic source, is typically accelerated to approximately 1200 in! sec where its kinetic energy is used to drive the nail. The bumper absorbs the excess energy left over after the nail is driven. The bumper fulfills this function by converting kinetic energy into viscous strain energy and heat. All bumper designs must withstand repeated impacts. This often results in premature failure which can be traced to two mechanisms: the stresses are too high and! or the temperature rise in bumper results in degradation of the material properties. The objective of this application brief is to demonstrate how advanced analysis techniques were applied to a typical industrial staple gun bumper design (Figure 1.)

A nonlinear transient dynamic analysis was conducted with the ABAQUS! Standard program. The bumper was modeled with axisymmetric continuum elements, while the steel base restraint, cylinder wall and piston were represented by geometrical rigid surfaces. The bumper is positioned at the bottom of the cylinder and the piston is given an initial velocity of 1200 in!sec. An appropriate mass was assigned to the piston rigid surface. Contact between the bumper, piston and base restraint was modeled with contact surfaces which allow for arbitrary contact and frictional sliding. The material response of the bumper was represented by a rubber elasticity model which includes rate dependent behavior. In order to characterize the rate effects, the load-displacement of the piston was measured using optical methods and this data was used to calibrate the model until the numerical prediction matched the measured response.

The maximum tensile stresses illustrated in Figure 2 are depicted at the moment the piston motion has been stopped. Experience has shown that when peak tensile stresses exist at a free surface, premature fatigue failure is likely. The steady state temperature distribution shown in Figure 3 is due to repeated impacts (2/sec). Internal heat generation due to viscous effects is the sole source of material heating considered in this heat transfer analysis. The peak temperature is located inside the bumper due to the convective cooling effects at the free surfaces. In this particular case the maximum temperature is relatively low, but it is not uncommon for the bumper to fail due to material degradation and melt down. The loss of kinetic energy due to these viscous effects is clearly depicted in Figure 4.

Dr. A/an Leewood is president, AC Engineering, an engineering services company that provides practical solutions to mechanical design and analysis problems.

Datapoint Testing Services video extensometer

In the measurement of stress-strain data using a tensile tester, contact extensometers are conventionally used to measure strain. While these clamp-on devices provide highly accurate strain measurements, they have drawbacks. The attachment, usually knife-edged, tends to nick the surfaces of plastic specimens, creating regions of stress concentration which can lower the measured yield and tensile strength. This can affect the development of the failure criteria for the material, resulting in an underprediction of the yield behavior of the material.

Datapoint’s new Instron Video Extensometer represents the state-of-the-art in non-contact strain measuring devices. A video camera focused on the test specimen continuously records and digitizes strain data, producing high quality data free from instrument artifact. Weak specimens, such as films and elastomers that cannot bear the weight of a conventional extensometer, can now be tested. Additionally, since the sensing device is remote, the instrument can be used with equal accuracy over a wide range of temperatures, from -70 C to 250CC. Poisson’s ratio measurements can also be made between -40 C and 150 C.

This video extensometer is particularly useful for hyperelastic measurements where its large field of view lens can be used to measure Strains of several hundred percent. CAE analysts working on elastomers use this proecise information for large deformation structural analysis of elastic components. The . technology also fulfils the needs of blow mold ing and thermoforming simulations which need high temperature hyperelastic data for their material models.

Material models in impact analysis

Automotive crashworthiness impact situations, such as those described in NHTSA’s FMVSS2O1, commonly involve polymeric materials designed to withstand high levels of energy while providing minimum injury to the occupant. Dynamic impact simulation software packages such as LS-Dyna3D, routinely used to analyze such impact situations, offer a range of material models to represent different material behaviors. For accurate results from an impact simulation, the user must carefully choose the constitutive model that best represents the mechanical behavior of the materials involved.

This article evaluates three rate-sensitive material models within LS-Dyna3D for use in modeling a polypropylene copolymer material for an ‘A” pillar. This impact situation is analyzed under a worst-case scenario: a generic “A” pillar resting on a non-compliant plate of steel. Injury to the head is calculated using the “heading injury criteria” (HIC), as obtained from the deceleration of the head over the duration of the impact event.

Experimental Procedure

The impact event shown in Figure 1 involves a 4.5 kg, 152 mm diameter steel ball impacting a polypropylene ribbed plaque placed on a 25 mm thick steel plate. The velocity of the steel ball is 6.7 m/s. The plaque has ribs spaced 19 mm apart with two longitudinal ribs. An accelerometer was embedded in the steel ball for acceleration measurement. Raw test data was filtered at SAE Class 1000, or 10 kHz.

Models vs. Experimental Results

Material Model 24 Is a piecewise-linear, strain-rate dependent isotropic plasticity model. A stress-strain curve is represented by an elastic modulus with the plastic region described as multiple piecewise linear segments. While individual curves can be defined for each strain rate, only a single elastic modulus can be used. Figure 2 shows the results of the simulation using Material Model 24 superimposed on three experimental results. For this scenario, the results are deceivingly good, with the medium elastic modulus case predicting a peak acceleration value within 1% of experimental, and a HIC value less than 1% of experimental results.

Closer examination of Figure 2 indicates that the simulation corresponds well with experimental results only between 0.105 and 0.1053 sec. Beyond this, simulation predicts a much softer response. Also, failure occurred at the rib intersections during the test, presumably at approximately 0.5 msec into the event. Since the simulation was run without using a failure option, its close peak acceleration and HIC predictions appear almost coincidental. This material model allows for the use of a failure option by specifying a failure strain value which is not rate sensitive.

A second series of simulations was conducted using Material Model 103 which is an anisotropic viscoplastic model with piecewise-linear, strain rate dependency. The results for this series of analyses are shown in Figure 3. While the peak acceleration and HIC predictions are not as good as those from Material Model 24, the initial portion of the acceleration curve corresponds more closely with the experiment, until failure occurs. Again, a failure option was not used with this model since it is not rate sensitive.

The final material model analyzed is a bi-linear, strain rate dependent, isotropic plasticity model referred to as Material Model 19 within LS-Dyna3D. A stress-strain curve is represented as two linear segments (elastic and plastic), described by an elastic modulus and a plastic modulus. Multiple bi-linear curves can be defined for each strain rate. Poisson’s ratio, density and optional failure criteria (von Mises failure stress as a function of strain rate), are defined. Simulation results shown in Figure 4, using Material Model 19, were more encouraging. When not using a failure option, simulation predicts a response similar to that obtained from Material Model 103. However, when using a failure option, simulation results are much closer. With a failure (von Mises) stress of 7,000 psi at the highest strain rate, the predicted peak acceleration and HIC values are within 1% and 4%, respectively. The entire acceleration curve more closely corresponds with experimental than any of the previous simulation results.

It is theorized that Model 19 provides better results than the other material models because the elastic modulus, yield stress, yield strain and failure stress are all rate dependent. Also, plastic strain-rates seen in the ribs exceed the maximum strain-rate in the material model. As a result, the bi-linear model, which over predicts stiffness, may be compensating for the lack of higher strain-rate data in the material model.

Summary

Careful selection of constitutive models plays a crucial role in accurate predictions of structural responses from simulation. This study indicates that failure (and/or damage) properties for the test material must be properly accounted for in the simulation, and that in the absence of such properties, misleading predictions can result. Further, the ultimate failure stress or strain obtained from a tensile test is highly idealized, and is not adequate for proper prediction of failure. A failure stress obtained from a tn-axial stress state, as seen in this ribbed plaque study, is more appropriate for accurate predictions.

Jim Lorenzo is a Research Engineer in the Engineenng Design Group at Monte/I USA. Jim has a BSME from Cleveland State University and an MSME from Bucknell University He has over 10 years of experience in the plastics industry.

Generating high speed stress-strain data for impact simulation

Three-point bending has shown promise as an economical means of obtaining high-strain rate properties of materials.

In a paper presented last fall at the International Body Engineer’s Conference (IBEC) in Stuttgart, Germany, Hubert Lobe and Jim Lorenzo showed that high strain-rate properties of plastics could be measured using a pendulum tester (Instron Dynatup POE 2000), configured for three-point bending. With this set up, they were able to obtain data at strain rates of 4800o Is. The applicability of the model was verified with an instrumented multi- axial bounce impact test. However, the pendulum tester was limited in its range of strain rates.

High strain rates achieved

In recent work, Yogesh Potdar and Wei Zou, graduate students at Cornell University, sought to remove this limitation by performing the measurements using an Instron Dynatup falling dart tester configured for three point bending measurements. By reducing the span to half that used in the original work, they were able to achieve impact velocities up to 4 m/s, which translates to strain rates of 2250°c Is.

They point out that these strains are typical of those seen in impact situations. Radially clamped disks subjected to multi-axial impact at velocities of 2 rn/s and 4 rn/s experienced strain rates of 2600% Is and 5200°c /5.

Oscillation of the specimen

Potdar and Zou also investigated the issue of oscillation of the test bar at the instant of impact. They found that the calculated natural frequency of the beam corresponded with the frequency of the first oscillation observed on the experimental load-deformation traces.

The issue of oscillation or vibration has interesting implications for the analysis of impact situations. On one hand, such vibrations are typically observed when components are subjected to impact. On the other hand, material models cannot handle such complex behavioral characteristics, One solution is to damp out these transient effects using a smoothing function. This results in a representative curve without the transient oscillation. In fact, this was the approach used successfully in the original IBEC paper.

Datapoint Testing Services adds staff

Craig Montoya joined the company in December 1997. Craig has a BS degree and comes to Datapoint from
Borg Warner Automotive. His responsibilities include impact testing and pressure-volume- temperature measurements.

Mike Tylenda has been promoted to Maintenance Supervisor.

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