© 2014 CAE Associates

Time-Dependent Response of Plastics

– Case Study Accurate FEA of Engineering

Plastics Seminar

Tarrytown, NY

October 14, 2014

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Case Study: Plastic Cap

The response of a threaded plastic cap used to seal a water spigot is

investigated.

— Cap is threaded onto a pipe, compressing the washer to create a watertight

seal.

— Loading consists of the axial preload and internal water pressure.

— Structural response over a time of 2 years is predicted.

— Room temperature.

Cut-away of cap

connection assembly.

Plastic cap

Pipe

Washer

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Time-Dependent Modeling Approach

Many plastic materials exhibit creep behavior at room temperature.

Creep is the progressive deformation of a material at a constant stress.

— For engineering metals, creep is usually important at elevated temperatures

and under high stresses.

— Plastics can exhibit creep at room temperature.

Creep is normally assumed to have 3 steps:

— Primary – initial stage, usually has high rate of creep strain.

— Secondary – constant rate.

— Tertiary – creep failure.

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Time-Dependent Modeling Approach

In finite element analyses, the modeling of creep includes the effect of

stress relaxation.

— Accumulation of creep strain will either increase the total strain (i.e. creep) or

reduce the elastic strain (i.e. relaxation).

Stress relaxation is the decrease of stress in a material under constant

strain.

Since a given point in the finite element model is not exactly perfectly

stress-controlled or strain-controlled, the analysis will predict the creep and

relaxation response from the same creep data and calculate the

appropriate stress and strain behavior.

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Time-Dependent Modeling Approach

Creep rupture data represents the time to failure of a material under a

given stress.

— By predicting the stress distribution in a structure over time, these stresses can

be compared to stress rupture data to determine the structural integrity.

— Can be used to determine the factor of safety of a design.

An example creep rupture plot is shown below.

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Geometry Definition

The physical geometry is axisymmetric except for the threads, which spiral

down the inner wall of the cap and the outer wall of the pipe.

Because the pitch of the threads typically results in a very shallow slope of

the thread, and since the expected behavior in the washer and the corner

region of the cap (high stress region) will essentially be axisymmetric, a 2D

axisymmetric model is used.

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Load Definition

The design loading is defined as:

— Axial preload = 70 lbs.

— Internal water pressure = 75 psi.

The preload is applied using a bolt pretension loading on the pipe.

— The pretension elements will extend the pipe into the washer until the specified

preload magnitude is reached.

— Once the preload is reached, the extension distance is locked.

— The preload can change over time based on the response of the structure.

Once the preload and water pressure are applied, creep effects are turned

on and the analysis is performed out to 2 years.

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Material Property Definition

The following material properties are used for the analysis:

— Elastic-plastic stress-strain curve for the plastic cap material.

— Creep material law for the plastic cap material.

— Hyperelastic material law for the washer.

— Linear elastic material properties for the pipe.

Stress-strain data used in the analysis:

— Data must be translated to true stress – log strain for large strain response.

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Material Property Definition

Creep data used in the analysis:

— Creep data is creep strain accumulated as a function of time for various stress

levels, using room temperature data for this application.

— A creep law is then used to fit the creep data.

• The creep law extends the data to any stress level.

The creep law used in this analysis is a combined time-hardening creep

law that models primary and secondary creep:

— The constants in the creep law are found from a nonlinear regression analysis

to fit the data.

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Mesh Definition

2D axisymmetric mesh is shown.

— Finer mesh used in the expected region of high stress.

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Displacement Results

The plot below shows the displacement sum contour plot at the end of the

analysis (2 years).

— Note the compression of the washer forming the watertight seal.

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Stress Results

The maximum principle stress contour is shown at the end of the

application of the preload:

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Stress Results

The maximum principle stress contour is shown at the end of the

application of the water pressure:

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Stress Results

The maximum principle stress contour is shown at the end of 2 years:

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Preload As Function of Loading/Time

A portion of the preload is lost over time due to deformation of the cap.

— Time is shown with log scale in hours due to time period of 2 years.

Preload Water Pressure

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Strain As Function of Loading/Time

A plot of the elastic, plastic, creep and total strain at the maximum stress

location.

Preload Water Pressure

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Stress As Function of Loading/Time

Below is a plot of the maximum value of the maximum principle stress over

the range of time, with creep rupture data superimposed:

Preload Water Pressure

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Conclusions

Based on the results of the time-dependent analysis of the plastic cap

assembly:

— The stresses after preload and water pressure application are below static

failure limits and creep rupture limits.

— Over time, even though the maximum stress in the cap is reduced due to a

combination of creep deformations that tend to reduce the preload and

relaxation of the plastic, the remaining stress level reaches the creep rupture

limit at approximately 10-100 hours.

— This analysis approach does not indicate catastrophic failure of the cap at this

time, but it indicates that failure will initiate at the high stress region.

— Life assessment indicates that the long-term structural integrity is in question,

and it is preferred that the calculated stresses would provide an adequate

factor of safety for creep rupture.

— Recommended design change: Eliminate lower threads that form notches in

high stress region.