12.7 Damage Boundary Curve

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12.7.1 Definition

Products are placed in a package to be protected from possible free-fall drops and impacts onto a floor or

a shipping platform during transport or handling. This packaging is often made up of a cushioning

material (for example, honeycomb or foam) which absorbs the impact energy (related to the impact

velocity) either by inelastic deformation, and which generates a shock at the entry of the material, whose

12-26 Vibration and Shock Handbook

© 2005 by Taylor & Francis Group, LLC

shape is often comparable to a rectangular or a trapezoid pulse (Figure 12.30). Alternatively, it can be

made of an elastic material, which produces at the material entry a shock with a near half-sine waveform.

After determination of the shock environment, a statistical analysis allows one to specify the design

drop height, with a given percentage of loss tolerated.

To choose the characteristics of the cushioning material constituting the package, it is first of all

necessary to determine the shock fragility of the product that would be subjected to a shock with one of

these two forms.

It can be considered that the severity of a shock is related to its amplitude and to its associated velocity

change (we saw that these two parameters intervene in the SRS). We thus determine the largest

acceleration and the largest velocity change that the unpackaged product subjected to these shocks can

support.

At the time of two series of tests carried out on a shock machine, we note, for a given acceleration, the

critical velocity change or, for a given velocity change, the critical maximum shock acceleration that leads to

a damage on the material (deformation, fracture, faulty operation after the shock, etc.).

Results are expressed on a diagram of the acceleration – velocity change by a curve defined as the

damage boundary curve (DBC; ASTM D3332), as shown in Figure 12.31.

Variable velocity change tests begin with a short-duration shock, then the duration is increased (by

preserving constant acceleration) until the appearance of damage (functional or physical). The critical

velocity change is equal to the velocity change just lower than that producing damage (ASTM, 1994).

The variable acceleration tests are performed on

a new material, starting with a small acceleration

level and with a rather large velocity change

(at least 1.5 times the critical velocity change

previously determined).

The tests should be carried out in the more

penalizing impact configuration (unit orientation).

12.7.2 Analysis of Test Results

Damage can occur if the acceleration and the

velocity change are together higher than the

critical acceleration and the critical velocity

change.

From the critical velocity change, the critical

drop height can be calculated. If Vi is the impact

velocity, VR is the rebound velocity, and a is the

Input Shock

Cushion

Material

Package

Product

Vi

Product

FIGURE 12.30 Shock transmitted to product during the crushing of package.

Acceleration

Acr

ΔVcr Velocity Change

Product Fragility

Critical Velocity

Damage

FIGURE 12.31 Damage boundary curve (rectangular

shock pulse).

Mechanical Shock 12-27

© 2005 by Taylor & Francis Group, LLC

rate of rebound ðVR ¼ 2aViÞ; the velocity change

DV is equal to

DV ¼ VR 2 Vi ¼ 2ðVi þ aViÞ

¼ 2ð1 þ aÞVi ð12:17Þ

and the free-fall drop height Hcr to

Hcr ¼

V 2

i

2g ¼

DV 2

2gð1 þ aÞ2 ð12:18Þ

If this critical height is lower than the design

height defined from the real use conditions of the

product, it is necessary to use a package with a

medium cushioning and then to define its

characteristics (crush stress, thickness) so that maximum acceleration at the time of impact is lower

than the critical acceleration. If not, no protection is necessary.

Tests are in general carried out with a rectangular shock waveform, for two reasons.

* As the rectangular shock is most severe (see SRSs), the result is conservative, as seen in Figure 12.32.

* The DBC is made up only of two lines, which makes it possible to determine the curve from only two

set of tests (saving time) by destroying only two specimens. A much more significant number of sets

of tests would be necessary to determine the curve from a half-sine shock waveform.

Note: If, for cost reasons, the same product is used to determine the critical velocity change or the

critical acceleration, it undergoes several shocks before failure. The test result is usable only if the product

fails in a brittle mode. If the material is ductile, each shock damages the product by an effect of fatigue,

which should be taken into account (Burgess, 1996, 2000).

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