FAQ: Can Shock or Vibration be used to Cover Acceleration?

Introduction

Neither shock nor vibration response should be used to cover rigid-body acceleration because material limits depend on the strain rate and on the duration of the load.

Furthermore, static deflection shapes differ from dynamic mode shapes.

Material Stress Limits

The following is an excerpt from Reference 1 with some minor editing:

A material can sometimes sustain an important dynamic load without damage, whereas the same load, statically, would lead to plastic deformation or to failure.  Many materials subjected to short duration loads have ultimate strengths higher than those observed when they are static.

Hopkinson noted that copper and steel wire can withstand stresses that are higher than their static elastic limit and are well beyond the static ultimate limit without separating proportionality between the stresses and the strains.  This is provided that the length of time during which the stress exceeds the yield stress is of the order of 1 millisecond or less.

From tests carried out on steel (annealed steel with a low percentage of carbon) it was noted that the initiation of plastic deformation requires a definite time when stresses greater than the yield stress are applied.  It was observed that this time can vary between 5 milliseconds (under a stress of approximately 352 MPa) and 6 seconds with approximately 255 MPa; with the static yield stress being equal to 214 MPa).  Other tests carried out on five other materials showed that this delay exists only for materials for which the curve of static stress deformation presents a definite yield stress, and the plastic deformation then occurs for the load period.

The equivalent units are as follows

Table 1.  Annealed Steel Test Results
Parameter	Stress  (MPa)	Stress (ksi)
5 msec for plastic deformation onset	352	51.1
6 sec for plastic deformation onset	255	37.0
Static Yield Stress	214	31.1

Dynamic Strength

Reference 2 notes:

As far as steels and other metals are concerned, those with lower yield strength are usually more ductile than higher strength materials.  That is, high yield strength materials tend to be brittle.  Ductile (lower yield strength) materials are better able to withstand rapid dynamic loading than brittle (high yield strength) materials.  Interestingly, during repeated dynamic loadings low yield strength ductile materials tend to increase their yield strength, whereas high yield strength brittle materials tend to fracture and shatter under rapid loading.

Reference 2 includes the following table where the data was obtained for uniaxial testing using an impact method.

Dynamic Strengthening of Materials

Material	Static Strength (psi)	Dynamic Strength (psi)	Impact Speed (ft/sec)
2024 Al (annealed)	65,200	68,600	>200
Magnesium Alloy	43,800	51,400	>200
Annealed Copper	29,900	36,700	>200
302 Stainless Steel	93,300	110,800	>200
SAE 4140 Steel	134,800	151,000	175
SAE 4130 Steel	80,000	440,000	235
Brass	39,000	310,000	216

Shock vs. Acceleration

The following paragraph is taken from Reference 3.

Acceleration loads are expressed in terms of load factors which, although dimensionless, are usually labeled as “g” loads. Shock environments (methods 516.5 and 517) are also expressed in “g” terms. This sometimes leads to the mistaken assumption that acceleration requirements can be satisfied by shock tests or vice versa. Shock is a rapid motion that excites dynamic (resonant) response of the materiel but with very little overall deflection (stress). Shock test criteria and test methods cannot be substituted for acceleration criteria and test methods or vice versa.

References

1.  C. Lalanne, Sinusoidal Vibration (Mechanical Vibration and Shock), Taylor & Francis, New York, 1999.

2.  R. Huston and H. Josephs, Practical Stress Analysis in
Engineering Design, Dekker, CRC Press, 2008.  See Table 13.1.

3.  MIL-STD-810F, Method 513.5, Section 1.3.3 Acceleration versus shock

Further information is given at:  Vibrationdata Acceleration Page

– by Tom Irvine