designing plastic parts for assembly

Designing Plastic Parts for Assembly

Paul A. Tres

ISBN 3-446-40321-3

Leseprobe

Weitere Informationen oder Bestellungen unter http://www.hanser.de/3-446-40321-3 sowie im Buchhandel

Seite 1 von 1Produktinformation

05.05.2006http://www.hanser.de/deckblatt/deckblatt1.asp?isbn=3-446-40321-3&style=Leseprobe

3 Strength of Material for Plastics

3.1 Tensile Strength

Tensile strength is a material’s ability to withstand an axial load.In an ASTM test of tensile strength, a specimen bar (Figure 3-1) is placed in a tensile

testing machine. Both ends of the specimen are clamped into the machine’s jaws, whichpull both ends of the bar. Stress is automatically plotted against the strain. The axial loadis applied to the specimen when the machine pulls the ends of the specimen bar inopposite directions at a slow and constant rate of speed. Two different speeds are used:0.2 in. per minute (5 mm/min) to approximate the material’s behavior in a hand assembly operation; and 2.0 in. per minute (50 mm/min) to simulate semiautomatic or automaticassembly procedures. The bar is marked with gauge marks on either side of the mid point of the narrow, middle portion of the bar.

As the pulling progresses, the specimen bar elongates at a uniform rate that is propor-tionate to the rate at which the load or pulling force increases. The load, divided by thecross-sectional area of the specimen within the gage marks, represents the unit stress resistance of the plastic material to the pulling or tensile force.

Figure 3-1 Test specimen bar

3.2 Compressive Stress 45

The stress (σ-sigma) is expressed in pounds per square inch (psi) or in Mega Pascals(MPa). 1 MPa equals 1 Newton per square millimeter (N/mm2). To convert psi into MPa,multiply by 0.0069169. To convert MPa into psi, multiply by 144.573.

F TENSILE LOAD= =

A AREAσ (3.1)

Proportional limitElastic limit

Yield point Ultimate stress

Strain

Stress

psi(MPa)

%

3.1.1 Proportional Limit

The proportional relationship of force to elongation, or of stress to strain, continues untilthe elongation no longer complies with the Hooke’s law of proportionality. The greateststress that a plastic material can sustain without any deviation from the law ofproportionality is called proportional stress limit (Figure 3-2).

3.1.2 Elastic Stress Limit

Beyond the proportional stress limit the plastic material exhibits an increase in elongationat a faster rate. Elastic stress limit is the greatest stress a material can withstand withoutsustaining any permanent strain after the load is released (Figure 3-2).

3.1.3 Yield Stress

Beyond the elastic stress limit, further movement of the test machine jaws in oppositedirections causes a permanent elongation or deformation of the specimen. There is a point beyond which the plastic material stretches briefly without a noticeable increase in load.This point is known as the yield point. Most unreinforced materials have a distinct yieldpoint. Reinforced plastic materials exhibit a yield region.

Figure 3-2 Typical stress/strain diagramfor plastic materials


It is important to note that the results of this test will vary between individualspecimens of the same material. If ten specimens made out of a reinforced plasticmaterial were given this test, it is unlikely that two specimens would have the same yieldpoint. This variance is induced by the bond between the reinforcement and the matrix material.

3.1.4 Ultimate Stress

Ultimate stress is the maximum stress a material takes before failure.Beyond the plastic material’s elastic limit, continued pulling causes the specimen to neck

down across its width. This is accompanied by a further acceleration of the axial elongation(deformation), which is now largely confined within the short necked-down section.

The pulling force eventually reaches a maximum value and then falls rapidly, with littleadditional elongation of the specimen before failure occurs. In failing, the specimen testbar breaks in two within the necking-down portion. The maximum pulling load,expressed as stress in psi or in N/mm2 of the original cross-sectional area, is the plasticmaterial’s ultimate tensile strength (σULTIMATE).

The two halves of the specimen are then placed back together, and the distancebetween the two marks is measured. The increase in length gives the elongation,expressed in percentage. The cross-section at the point of failure is measured to obtainthe reduction in area, which is also expressed as percentage. Both the elongationpercentage and the reduction in area percentage suggest the material ductility.

In structural plastic part design it is essential to ensure that the stresses that wouldresult from loading will be within the elastic range. If the elastic limit is exceeded,permanent deformation takes place due to plastic flow or slippage along molecular slipplanes. This will result in permanent plastic deformations.

3.2 Compressive Stress

Compressive stress is the compressive force divided by cross-sectional area, measured inpsi or MPa.

It is general practice in plastic part design to assume that the compressive strength of aplastic material is equal to its tensile strength. This can also apply to some structuraldesign calculations, where Young’s modulus (modulus of elasticity) in tension is used,even though the loading is compressive.

The ultimate compressive strength of thermoplastic materials is often greater than theultimate tensile strength. In other words, most plastics can withstand more compressivesurface pressure than tensile load.

The compressive test is similar to that of tensile properties. A test specimen is compressed to rupture between two parallel platens. The test specimen has a cylindricalshape, measuring 1 in. (25.4 mm) in length and 0.5 in. (12.7 mm) in diameter. The load is applied to the specimen from two directions in axial opposition. The ultimatecompressive strength is measured when the specimen fails by crushing.

3.2 Compressive Stress 47

A stress/strain diagram is developed during the test, and values are obtained for thefour distinct regions: the proportional region, the elastic region, the yield region, and theultimate (or breakage) region.

The structural analysis of thermoplastic parts is more complex when the material is incompression. Failure develops under the influence of a bending moment that increases as the deflection increases. A plastic part’s geometric shape is a significant factor in its capacity to withstand compressive loads.

P COMPRESSIVE FORCE= =

A AREAσ (3.2)

Figure 3-3 Compressive test specimen

The stress/strain curve in compression is similar to the tensile stress/strain diagram,except the values of stresses in the compression test are greater for the correspondingelongation levels. This is because it takes much more compressive stress than tensilestress to deform a plastic.

3.3 Shear Stress

Shear stress is the shear load divided by the area resisting shear. Tangential to the area,shear stress is measured in psi or MPa.

There is no recognized standard method of testing for shear strength (τ-tau) of a thermo-plastic or thermoset material. Pure shear loads are seldom encountered in structural partdesign. Usually, shear stresses develop as a by-product of principal stresses, or wheretransverse forces are present.


The ultimate shear strength is commonly observed by actually shearing a plastic plaquein a punch-and-die setup. A ram applies varying pressures to the specimen. Theram’s speed is kept constant so only the pressures vary. The minimum axial loadthat produces a punch-through is recorded. This is used to calculate the ultimate shear stress.

Exact ultimate shear stress is difficult to assess, but it can be successfully approximatedas 0.75 of the ultimate tensile stress of the material.

Q SHEAR LOAD=

A AREAτ = (3.3)

Q

Q

3.4 Torsion Stress

Torsional loading is the application of a force that tends to cause the member to twist about its axis (Figure 3-5).

Torsion is referred to in terms of torsional moment or torque, which is the product ofthe externally applied load and the moment arm. The moment arm represents the distancefrom the centerline of rotation to the line of force and perpendicular to it.

The principal deflection caused by torsion is measured by the angle of twist or by thevertical movement of one side.

Figure 3-4 Shear stress sample specimenexample: (a) before; (b) after

Figure 3-5 Torsion stress

3.4 Torsion Stress 49

When a shaft is subjected to a torsional moment or torque, the resulting shear stress is:

t tM M r= =

J Iτ (3.4)

Mt is the torsional moment and it is:

tM F R= (3.5)

The following notation has been used:J polar moment of inertiaI moment of inertiaR moment armr radius of gyration (distance from the center of section to the outer fiber)F load applied

3.5 Elongations

Elongation is the deformation of a thermoplastic or thermoset material when a load is applied at the ends of the specimen test bar in opposite axial direction.

The recorded deformation, depending upon the nature of the applied load (axial, shear or torsional), can be measured in variation of length or in variation of angle.

Strain is a ratio of the increase in elongation by initial dimension of a material. Again,strain is dimensionless.

Depending on the nature of the applied load, strains can be tensile, compressive, or shear.

L= (%)

Lε

Δ(3.6)

3.5.1 Tensile Strain

A test specimen bar similar to that described in Section 3.1 is used to determine thetensile strain. The ultimate tensile strain is determined when the test specimen, beingpulled apart by its ends, elongates. Just before the specimen breaks, the ultimate tensilestrain is recorded.

The elongation of the specimen represents the strain (ε-epsilon) induced in the material,and is expressed in inches per inch of length (in/in) or in millimeters per millimeter (mm/mm). This is an adimensional measure. Percent notations such as ε = 3% can also beused. Figure 3-2 shows stress and strain plotted in a simplified graph.


Figure 3-7 Compressive specimen showing dimensional change in length. L is the original length; P is the compressive force. ΔL is the dimensional change in length

Figure 3-6 Tensile specimen loaded showingdimensional change in length. The differencebetween the original length (L) and theelongated length is ΔL

3.5 Elongations 51

3.5.2 Compressive Strain

The compressive strain test employs a set-up similar to the one described in Section 3.2.The ultimate compressive strain is measured at the instant just before the test specimenfails by crushing.

3.5.3 Shear Strain

Shear strain is a measure of the angle of deformation γ – gamma. As is the case withshear stress, there is also no recognized standard test for shear strain.

Q

Q

Q

Q

γ

Figure 3-8 Shear strain: (a) before; (b) after

3.6 True Stress and Strain vs. Engineering Stress and Strain

Engineering strain is the ratio of the total deformation over initial length.Engineering stress is the ratio of the force applied at the end of the test specimen by

initial constant area.True stress is the ratio of the instantaneous force over instantaneous area.Formula 3.7 shows that the true stress is a function of engineering stress multiplied by

a factor based on engineering strain.

( )TRUE = +1σ σ ε (3.7)

True strain is the ratio of instantaneous deformation over instantaneous length.Formula 3.8 shows that the true strain is a logarithmic function of engineering strain.

( )TRUE = +ln 1ε ε (3.8)


By using the ultimate strain and stress values, we can easily determine the true ultimatestress as:

( )1TRUEULTIMATE ULTIMATE ULTMATE= +σ σ ε (3.9)

Similarly, by replacing engineering strain for a given point in Equation 3.8with engineering ultimate strain, we can easily find the value of the true ultimate strainas:

( )ln 1TRUEULTIMATE ULTIMATE= +ε ε (3.10)

Both true stress and true strain are required input as material data in a variety of finiteelement analyses, where non-linear material analysis is needed.

Initialarea

Reducedarea

3.7 Poisson’s Ratio

Provided the material deformation is within the elastic range, the ratio of lateral tolongitudinal strains is constant and the coefficient is called Poisson’s ratio.

LATERAL STRAIN=

LONGITUDINAL STRAINν (3.11)

In other words, stretching produces an elastic contraction in the two lateral directions.If an elastic strain produces no change in volume, the two lateral strains will be equal tohalf the tensile strain times –1.

Figure 3-9 True stress necking-down effect

3.7 Poisson’s Ratio 53

bb

b'b'

L

L

Δ

Under a tensile load, a test specimen increases (decreases for a compressive test) inlength by the amount ΔL and decreases in width (increases for a compressive test) by theamount Δb. The related strains are:

LONGITDINAL

LATERAL

=

=

L

Lb

b

Δε

Δε

(3.12)

Poisson’s ratio varies between 0, where no lateral contraction is present, to 0.5 for which the contraction in width equals the elongation. In practice there are no materials with Poisson’s ratio 0 or 0.5.

Table 3-1 Typical Poisson’s ratio values for different materials

Material Type Poisson’s Ratio at 0.2 in./min (5 mm/min) Strain Rate

ABS 0.4155Aluminum 0.34Brass 0.37Cast iron 0.25Copper 0.35High density polyethylene 0.35

Figure 3-10 Dimensional change in only two ofthree directions


Table 3-1 (Continued)

Material Type Poisson’s Ratio at 0.2 in./min (5 mm/min) Strain Rate

Lead 0.45Polyamide 0.38Polycarbonate 0.3813% glass reinforced polyamide 0.347Polypropylene 0.431Polysulfone 0.37Steel 0.29

The lateral variation in dimensions during the pull-down test is:

b = b b′Δ − (3.13)

Therefore, the ratio of lateral dimensional change by the longitudinal dimensionalchange is:

bb=L

L

Δ

νΔ

(3.14)

Or, by rewriting, the Poisson’s ratio is:

LATERAL

LONGITUDINAL

=ε

ν

ε

(3.15)

3.8 Modulus of Elasticity

3.8.1 Young’s Modulus

The Young’s modulus or elastic modulus is typically defined as the slope of thestress/strain curve at the origin.

The ratio between stress and strain is constant, obeying Hooke’s Law, within theelasticity range of any material. This ratio is called Young’s modulus and is measured inMPa or psi.

STRESSE = = = CONSTANT

STRAIN

σ

ε

(3.16)

Hooke’s Law is generally applicable for most metals, thermoplastics and thermosets,within the limit of proportionality.

designing plastic parts for assembly

Documents