Fatigue Failure of an Eyeglass Frame

In the search for weight reduction, the cross section of an eyeglass frame is continuously reduced. The thin section over the nose transfers the entire load between the two halves. This example predicts the fatigue life using the combined Basquin and Coffin-Manson model when eyeglasses are subjected to bending.

Model Definition

The frame of the eyeglasses is made of the MONEL alloy 400. The eyeglass lenses are made of a CR-39 material that is lighter in weight than glass. The risk of fatigue in the lenses is avoided by using a coating that holds together any shards in case of fracture. Therefore only the fatigue life of the frame is predicted.

The frame of the eyeglasses is very thin, 1 mm, and has a shape according to Figure 1.

Figure 1: Shape of the eyeglasses.

Young’s modulus of the MONEL alloy 400 is taken from the COMSOL Material Library and the Poisson’s ratio is 0.32. For the CR-39 material, the Young’s modulus is 2.1 GPa and the Poisson’s ratio is 0.4.

Fatigue data for the MONEL alloy 400 has been obtained in rotating bending tests, and fitted to the combined Basquin and Coffin-Manson relation according to where the strain amplitude, εa, is expressed as

where εa is the strain amplitude, E is the Young’s modulus, N represents the number of cycles to failure, and σf’, εf’, b, and c are fatigue material parameters.

Bending of the eyeglasses is simulated by fixing one side of the eyeglasses and applying an alternating vertical 4 N force on the other side of the eyeglasses.

Results and Discussion

The stress distribution in the eyeglasses at the peak load is shown in Figure 2.

Figure 2: Equivalent stress in eyeglasses.

Bending of the eyeglasses causes high stresses on both sides of the thin central part. Since the equivalent stress does not discriminate between tension and compression the same stress levels are encountered on both sides. The resulting stress contours are similar if the bending is reversed when the right part of the glasses is pulled down instead.

Since the fatigue data is obtained in a rotating bending test, the stresses and strains alternate between tension and compression during one test cycle. This is exactly the same structural behavior as in one load cycle of the eyeglasses and therefore the fatigue curve is directly applicable to the resulting principal strains. The highest and smallest principal strains at peak loads are shown in Figure 3.

Figure 3: Principal strains in the eyeglasses. Above: first principal strain when pulling upward. Below: third principal strain when pulling downward.

When pulling up, the lower side of the thin central section experiences peak tensile strains. The peak compressive strains are experienced in the same point when pulling the eyeglasses down. On the upper side of the thin central section over the nose, an opposite situation is encountered, with peak compression when pulling up and peak tension when pulling down. The difference in strain during both load events controls the fatigue life that is predicted in Figure 4. The estimated life is approximately 100,000 cycles.

Figure 4: Fatigue life computed by the combined Basquin and Coffin-Manson relation.

Fatigue_Module/Strain_Life/eyeglass_frame_fatigue

Modeling Instructions

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Geometry 1

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Import 1 (imp1)

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Browse to the model’s Application Libraries folder and double-click the file eyeglass_frame_fatigue.mphbin.

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The thin central part of the eyeglasses transfers the entire load between the two halves. Make a rectangle in the center to create a domain for fine structured mesh.

Rectangle 1 (r1)

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In the text field, type 10.

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Materials

Monel 400 [solid,annealed] (mat1)

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In the table, enter the following settings:


Property	Variable	Value	Unit	Property group
Density	rho	0.32	kg/m³	Basic

CR-39

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In the window for , type CR-39 in the text field.

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Locate the section. In the table, enter the following settings:


Property	Variable	Value	Unit	Property group
Young’s modulus	E	2.1[GPa]	Pa	Young’s modulus and Poisson’s ratio
Poisson’s ratio	nu	0.4	1	Young’s modulus and Poisson’s ratio
Density	rho	1.3[g/cm^3]	kg/m³	Basic

Solid Mechanics (solid)

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Fixed Constraint 1

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Boundary Load 1

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0	x
1	y

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Mesh 1

Mapped 1

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Distribution 1

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Study 1

Step 1: Stationary

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Click four times.

In the table, enter the following settings:


Load case	lg1	Weight
Load case 1	√	0
Load case 2	√	4
Load case 3	√	-4
Load case 4	√	0

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Results

Stress (solid)

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Surface 1

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Deformation

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Stress (solid)

The equivalent stress does not discriminate between tension and compression. Evaluate how strains change at peak loads.

Principal strain (solid)

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Surface 1

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Display both the largest principal strain and the smallest principal strain in the same figure.

Deformation

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Surface 2

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Deformation

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Add Physics

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Fatigue (ftg)

Strain-Life 1

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Materials

Monel 400 [solid,annealed] (mat1)

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In the table, enter the following settings:


Property	Variable	Value	Unit	Property group
Fatigue strength coefficient	sigmaf_Basquin	970[MPa]	Pa	Basquin
Fatigue strength exponent	b_Basquin	-0.077	1	Basquin
Fatigue ductility coefficient	epsilonf_CM	0.738	1	Coffin-Manson
Fatigue ductility exponent	c_CM	-0.54	1	Coffin-Manson