2Equivalent ThicknessWhen a thermoplastics is specified as a replacement for another material, the new part often needs to have the same stiffness as the old oneDeflection is proportional to 1/E*IE is modulusI is moment of inertiaI is proportional to thickness3
6Equivalent ThicknessCalculate the thickness of a part that when made of polycarbonate will have the same deflection as a 0.75mm thick aluminum part at 73deg using moduli of the two materials
7Equivalent ThicknessCalculate the thickness of a part that when made of polycarbonate will have the same deflection as a 0.75mm thick aluminum part at 73deg using thickness conversion factors
8Thermal StressThermal expansion and contraction are important considerations in plastic designExpansion-contraction problems often arise when two parts made of different materials having different coefficients of thermal expansion are assembled at temperatures other than the end use temperatureWhen the assembled part goes into service in the end use environment, the materials react differently, resulting in thermal stress
9Thermal StressThermal Stress can be calculated by:
12Thermal StressE = 300,000 psi for polycarbonateσ = 1000 psi
13Beam Analysis Alternate designs for park bench seat members Example of the method a designer will use to estimate bending stress, strain and deflectionsMaterial is recycled polyolefinDesign for two people, 220lbs each, for 8 hours per day10 year service life
15Beam AnalysisPlastics have the advantage of durability, through coloring and design flexibilityPlastics have the disadvantage of relatively low modulus values, particularly at elevated temperaturesDesigner must estimate the maximum stress and deflection for each of the proposed designsFailure could result in personal injuryCreep must be consider in the long term application
17Beam AnalysisSupportThe planks are beams resting on the bench supports that have an unsupported length of 48 inchesSupport conditions at both ends exhibit characteristics of both simple and fixed supportsA beam with simple supports represents the worst case for maximum possible mid-span stress and deflection
18Beam Analysis Loading conditions Bench is loaded and unloaded periodically, not continuousLoading is intermittent rather than fatigueLoads are staticWeight of the beam is of concern, due to creepAssume 2 people, 220 lbs each, for 8 hour per day distributed over the length of one beam
19Beam Analysis Loading conditions Full recovery is assumed to occur overnightThe size of the continuous, uniformly distributed load, due to the weight of the beam must be determinedThe deflection and stresses resulting from the intermittent external load are superimposed on the continuous uniformly distributed load caused by the weight of the beam
21Beam Analysis Equations Generalized equations for a beam with partially distributed loads and simple supports areAt L/2L length in inchesC distrance from the neutral axis to surfaceW is load in lbs/inE is the materials modulusI moment of inertia, in4M the bending moment,
22Beam Analysis Service Environment Used outdoors throughout the year Used in various climatesContacts various cleanersMaximum service temperature is assumed to be 100ºFService life is ten years
23Beam Analysis Material Properties In this application, the planks are loaded for extended periods of time and creep effects must be taken into accountThe appropriate creep modulus is used in the maximum deflection equationThe deflection and stress are due to both the beam weight and the external load
24Beam Analysis Material Properties Maximum deflection will occur at the end of the service life, 10 years, due to internal loadingE = 2.5 x 105 psiMaximum deflection will occur after 8 hours of continuous loading due to the external loadE = 3 x 105 psi
27Beam AnalysisThe external loading, uniformly distributed due to the weight of the two adults is the same for all four caseswe = 2*220lbs/48 inches = 9.17 lbs/inThe internal load change in each casewi = density*volume/lengthSolid = lbs/inHollow = lbs/inRib = lbs/inFoam = lbs/in
33Beam Analysis Comparisons Solid is lowest in stress and deflection, but the material and manufacturing costs are excessive and quality problems with voids and sink marksHollow offers a 50% material savings, but only a 26% increase in deflection and 28% increase in stressRib offers a 38% material savings and a 41% increase in deflection and 59% increase in stressesFoam offers a 20% material savings and 28% increase in deflection and 29% increase in stresses
35Living HingeA living hinge is a thin flexible web of material that joins two rigid bodies together.A properly designed hinge molded out of the correct material will never fail.Long-life hinges are made from polypropylene or polyethylene.If the hinge is not expected to last forever, engineering resins like nylon and acetal can be used.
36Figure: This polypropylene package for baby wipes utilizes a living hinge.
37Living HingeBefore designing a living hinge, it is important to understand how the physical properties relate to the hinge design calculations.There are three types of hinges:a fully elastic hinge, capable of flexing several thousand cyclesa fully plastic hinge, capable of flexing only a few cyclesand a combination of plastic elastic, capable of flexing hundreds of times
38Living HingeFigure 1: Typical stress/strain curve for metals and some plastics.
39Living HingeWhen a living hinge is flexed, the hinge's plastic fibers are stretched a certain amount, depending on its design. The amount of stretch is the crucial factor determining hinge life.To design a fully elastic hinge, the hinge's maximum strain must be in the elastic region of the curve; the plastic will fully recover its shape after a flex, and should last for many flexes.A plastic hinge design that experiences strain in the plastic region, will see permanent deformation, and will last only a few flexes.
40Living Hinge Figure 3: Dimensions for a right angle hinge. Figure 2: Dimensions for a 180 polypropylene and polyethylene living hinge.Figure 3: Dimensions for a right angle hinge.
41Living HingeHinges designed for polypropylene and polyethylene should follow dimensional guidelines to create a fully elastic hinge that will last forever.Figure 2 shows some general dimensions for a properly designed living hinge.Figure 3 shows dimensions for a right angle hinge
42Living HingeFigure 4: This is an example of a poorly designed hinge with no recess. When bent, the absence of a recess creates a notch.Figure 5: The recess on top of the hinge eliminates the notch when it is folded.
43Living HingeThe two major features of a living hinge are the recess on the top and the generous radius on the bottom.Figures 4 and 5 show the purpose of the recess.Many hinges are designed without a recess; as a result, when the hinge is bent 180, a notch is formed. This hinge design creates greater stress in the web, and the notch acts as a stress concentrator. Hinges designed this way will not last long.Figure 5 shows that with a recess, the notch is eliminated, and the web is able to fold over easier.
44Living HingeThe large radius on the bottom of hinge helps orient the polymer molecules as they pass through the hinge.Molecular orientation gives the hinge its strength and long life.Commonly, immediately after a hinge part is molded, the operator or a machine will flex the hinge a few quick times to orient the molecules while the part is still warm.
45Living HingeThe hinge dimensions for polyethylene and polypropylene are based on the materials' properties, including modulus, yield stress, yield strain, ultimate stress, and ultimate strain.Because other resins' properties vary widely, living hinge dimensions must be calculated for each particular resin.Figure 6 shows the dimensions that will be used in the calculations.
46Living HingeBasically, the calculations find the maximum strain in the hinge and compare it to the material properties.If the strain is below the elastic limit, the hinge will survive.If the strain is in the plastic region, the hinge will last a few cycles.If the strain is the past the breaking point, the hinge will fail.
47Living HingeSeveral simplifying assumptions are made, and tests have shown the assumptions are sound.1) The hinge bends in a circle and the neutral axis coincides with the longitudinal hinge axis.2) The outer fiber is under maximum tension; the inner fiber is under maximum compression.3) When the tension stress reaches the yield point, the hinge will fail by the design criteria.
48Living Hinge Refer to Figure 6. L1 = R (the perimeter of semicircle). L1:Length of the hinge's neutral axist:Half the hinge's thicknessl:Hinge recessR:Hinge radiusL0:Length of the hinge's outer fibers
49Living Hinge Figure 6 L1:Length of the hinge's neutral axis t:Half the hinge's thicknessl:Hinge recessR:Hinge radiusL0:Length of the hinge's outer fibers
50Living Hinge Elastic Hinge In a fully elastic hinge design, bending must be less than yieldand bending must be less than yield.Failure occurs whenbending = yieldand when bending=yield.Either equation can be used, depending on whether yield stress or strain is known.
51Living HingeTo use the equations, find the yield strain (yield), or the yield stress (yield) and secant modulus at yield (Esecant, yield).Substituting these values into the equations will result in the lowest value of L1 that will yield an elastic hinge.Either the hinge thickness or its length must be known as well.Generally, a minimum processing thickness is selected, ranging from 0.008" to 0.015", and then a length is calculated.
52Living Hinge Figure 6 Figure 7: Hinge dimensions for calculations L1:Length of the hinge's neutral axist:Half the hinge's thicknessl:Hinge recessR:Hinge radiusL0:Length of the hinge's outer fibersFigure 7: Hinge dimensions for calculations
53Living Hinge Plastic Hinge: A plastic hinge will only last a few cycles.Cracks will probably start on the first flex.Calculations for a plastic hinge are the same as those of for an elastic hinge, except ultimate and ultimate are used.
54Living Hinge Processing Conditions The key to living hinge life is to have the polymer chains oriented perpendicular to the hinge as they cross it.As stated earlier, parts are generally flexed a few times immediately after molding to draw and further orient the hinge molecules.Another important factor in determining orientation is gate location.It is crucial to maintain a flow front as parallel to the living hinge as possible.
55Living HingeFigure 9: An example of a poorly gated part.
56Living HingeFigure 10: A properly gated hinged part.Example of a properly gated part. A wide flash gate is placed on one end to create a flat flow front when the plastic reaches the hinge.This results in even flow over the hinge, and provides proper orientation direction.Locating a gate at the center of one end of the part would be another suitable gate location.
57Living HingeMaterial: Hoechst Celanese Acetal Copolymer, Grade TX90 Unfilled High ImpactTensile Strength at Yield: 45 MPaElongation at Yield: 15%2t (hinge thickness) = 0.012"l (hinge recess) = 0.010"This is a 180 hinge.Find the minimum hinge length for a fully elastic hinge.
58Living HingeFor a fully elastic hinge, the minimum hinge length is calculated usingL1 = (t) / yieldL1 = (0.006"* ) / 0.15L1 = 0.126" for a fully elastic hinge
59Living Hinge Material: Dupont Zytel 101 NC010 Nylon 66, Unfilled Tensile Strength at Yield: 83 MPaElongation at Yield: 5%Elongation at Break: 60%2t (hinge thickness) = 0.012"l (hinge recess) = .010" This hinge only has to bend 90.Find the minimum hinge length for a fully elastic design.
60Living HingeSince the bend is 90, can be substituted with /2 (this can be found from the previous derivation).L1 = (t/2) / yieldL1 = (0.006"* *0.5) / 0.05L1 = 0.188"For a 180 bend, L1 would need to be 0.376".This is probably not moldable.Even 0.188" may be difficult to mold.
62Snap FitSnap fits are the simplest, quickest and most cost effective method of assembling two partsWhen designed properly, parts with snap-fits can be assembled and disassembled numerous times without any adverse effect on the assembly.Snap-fits are also the most environmentally friendly form of assembly because of their ease of disassembly, making components of different materials easy to recycle.
64Snap FitMost engineering material applications with snap-fits use the cantilever designOther types of snap-fits which can be used are the “U“ or “L“ shaped cantilever snapsThese are used when the strain of the straight cantilever snap cannot be designed below the allowable strain for the given material
65Snap FitA typical snap-fit assembly consists of a cantilever beam with an overhang at the end of the beamThe depth of the overhang defines the amount of deflection during assembly.
66Snap FitThe overhang typically has a gentle ramp on the entrance side and a sharper angle on the retraction side.The small angle at the entrance side (α) helps to reduce the assembly effort, while the sharp angle at the retraction side (α“) makes disassembly very difficult or impossible depending on the intended function.Both the assembly and disassembly force can be optimized by modifying the angles mentioned above.
67Snap FitThe main design consideration of a snap-fit is integrity of the assembly and strength of the beam.The integrity of the assembly is controlled by the stiffness (k) of the beam and the amount of deflection required for assembly or disassembly.Rigidity can be increased either by using a higher modulus material (E) or by increasing the cross sectional moment of inertia (I) of the beam.The product of these two parameters (EI) will determine the total rigidity of a given beam length.
68Snap FitThe integrity of the assembly can also be improved by increasing the overhang depth.As a result, the beam has to deflect further and, therefore, requires a greater effort to clear the overhang from the interlocking hook.However, as the beam deflection increases, the beam stress also increases.This will result in a failure if the beam stress is above the yield strength of the material.
69Snap FitThus, the deflection must be optimized with respect to the yield strength or strain of the material.This is achieved by optimizing the beam section geometry to ensure that the desired deflection can be reached without exceeding the strength or strain limit of the material.
70Snap FitThe assembly and disassembly force will increase with both stiffness (k) and maximum deflection of the beam (Y).The force (P) required to deflect the beam is proportional to the product of the two factors:P= kYThe stiffness value (k) depends on beam geometry
71Snap Fit Stress or strain is induced by the deflection (Y) The calculated stress or strain value should be less than the yield strength or the yield strain of the material in order to prevent failure
75Snap FitThe cantilever beam formulas used in conventional snap-fit design underestimate the amount of strain at the beam/wall interface because they do not include the deformation in the wall itself.Instead, they assume the wall to be completely rigid with the deflection occurring only in the beam.This assumption may be valid when the ratio of beam length to thickness is greater than about 10:1.
76Snap FitHowever, to obtain a more accurate prediction of total allowable deflection and strain for short beams, a magnification factor should be applied to the conventional formula.This will enable greater flexibility in the design while taking full advantage of the strain-carrying capability of the material.
77Snap FitA method for estimating these deflection magnification factors for various snap-fit beam/wall configurations has been developedThe results of this technique, which have been verified both by finite element analysis and actual part testing, are shown graphicallyAlso shown are similar results for beams of tapered cross section (beam thickness decreasing by 1/2 at the tip).