2 Engineering Product Design

Transcription

1 115 Engineering Product Design When designing plstic components, success will depend on one prime fctor: how well we use the vriety of plstic properties nd the processing methods for obtining optimum results. The designer should select the best resin, relizing tht it is essentil for the resin s full potentil to be exploited to ensure tht the molded prt will stisfy both functionl nd cost requirements. Plstics re governed by the sme physicl lws nd the sme rules for good design s other mterils. These principles cn be pplied if the polymer properties re suitble for the operting environment of the product being considered. It is necessry to know nd understnd wht the end product must do nd under wht circumstnces it will operte, before design nlysis cn be done..1 Understnding the Properties of Mterils There is big difference between the properties, processing methods, nd pplictions of mterils mnufctured by vrious industries. There is not single mte ril tht cn be used for ll pplictions. Ech new outstnding property developed in mteril opens the door for new pplictions, technologies, nd innovtions tht will improve the efficiency nd qulity of life of the end users. Product designers should compre the properties of vrious groups of mterils (steels, thermoplstics, luminum lloys, rubber, etc.), becuse ech mteril hs different properties developed for specific pplictions nd mrkets nd uses different mnufcturing processes. All mterils hve benefits nd deficiencies (properties, processes, nd qulity), mking it difficult to compre the cost of finished products mde of different mterils nd processes. The mteril properties re directly relted to the end use pplictions whether or not one mteril is better thn nother. To illustrte this point, thermoplstic resin cnnot replce structurl steel bem used in building construction; the thermoplstic resins do not hve the strength, creep resistnce, or melt strength to be extruded into thick wlled shpes. Thermoplstic bems would lso wrp in ll directions. However, structurl bems cn be mde of thermoset composites, lthough this is expensive. In less criticl pplictions, such s the housing industry, wood composite structurl bems re replcing steel bems, becuse of their performnce nd light weight; they re esy to work with nd offer competitive price. A thermoplstic resin cnnot replce the steel in utomotive disc/drum brke housings, becuse the product requires dimensionl stbility, low therml expnsion, nd high strength nd rigidity t elevted tempertures. Thermoplstic resins do not meet the requirements. However, brke pds mde of thermoset polyimide hve been successfully used in irplnes. Metls cnnot replce utomotive rubber tires, bellows, diphrgms, or compression sels, becuse metls do not hve the elsticity, ftigue endurnce, wer resistnce, nd toughness of rubber. Metls re not used for light-weight nd compct cellulr phone housings, becuse metls re electricl conductors, hevy, corrosive, nd expensive.

2 116 Engineering Product Design Ferrous metls Nonferrous metls Thermosets Thermoplstics Ferrous metls Nonferrous metls Thermosets Thermoplstics Specific grvity Continuous exposure temperture ( F.) Ferrous metls Nonferrous metls Thermosets Thermoplstics Ferrous metls Nonferrous metls Thermosets Thermoplstics Ferrous metls Nonferrous metls Thermosets Thermoplstics Tensile strength (kpsi) Modulus of elsticity (Mpsi) Coefficient of liner therml expnsion (in/in/ F) x 1-6 Figure -1 Comprison of generic properties of mterils Automotive engine cst iron nd luminum intke mnifolds re being replced by fiber glss reinforced nylon to improve efficiency, lower weight, creting new mnufcturing processes, nd cost reduction. Automotive steel bumpers, externl side pnels, nd hoods hve been replced with TPE, thermoset composites, nd PC lloys to reduce weight, improve styling, nd reduce costs. Portble electricl tools nd smll kitchen pplince housings re no longer mde of die cst steel or luminum but hve been replced with nylon nd AS, improving toughness, electricl insultion, nd styling, lowering weight nd cost reduction. Wter fucet vlves mde of die cst steel, brss, or copper re being replced by new designs, updted styles, nd colors, using cetl, which elimintes corrosion, providing cost reduction nd opening new mrkets. High performnce, lrge size irrigtion vlves (from 1.5 to 3. in di.) nd smll vlves (.75 nd 1. in di.) mde of die cst steel nd brss were successfully replced with GR nylon 6/1 for the lrge vlves nd with GR nylon 6/6 or cetl for the smll vlves. This improved performnce nd relibility, eliminted corrosion, nd provided cost reduction. Other low performnce commercil vlves mde of rigid PVC (lower cost) re lso produced for the irrigtion mrket. Toilet nti-siphon (bllcock) vlves mde of severl brss nd copper components were replced with multi-functionl design in cetl, improving performnce, eliminting corrosion, nd providing cost reduction. The cetl vlves hd excellent performnce over 3 yer period. The comprison of properties is n effective tool when pplied to mterils in the sme fmily. To illustrte the point tht properties between different mteril fmilies cnnot be compred, Figure -1 shows severl grphs using different generic property vlues of the different mteril fmilies. The ferrous metl brs include cst iron, cold rolled steels, structurl steels, lloy steels, stinless steels, nd tool steels. The nonferrous metl brs include mgnesium, luminum, copper, nickel nd brss lloys, nd titnium. The rubber brs include crylic, butdiene, butyl, chloroprene, nitrile, silicone, urethne, EPDM, EPM, fluorocrbon, nd nturl rubbers. The thermoset brs include phenolics, silicones, lkyds, DAP, polyimides, minos, unsturted polyesters, epoxies, nd urethnes. The thermoplstic brs include AS, crylics, cetls, nylons, LCP, PT, PET, PS, PE, PP, PC, PPO, PEI, PEKK, PSU, PPS, PTFE, PVC, nd SAN. The specific grvity grph shows the unit weight of mteril compred to wter nd revels tht metls re two to eight times hevier thn plstics. On strength-to-weight bsis, plstics hve more fvorble position, s indicted by the specific grvity grph. In generl, the cost of metls is much higher thn plstics. The continuous exposure temperture grph shows tht metls hve wider temperture rnges thn plstics; metls cn be used t colder nd t elevted tempertures. This property is used for the clssifiction nd temperture rnge of plstics. The tensile strength (kpsi) grph shows tht metls re much stronger thn plstics; metls resist higher forces when being pulled prt before breking. The tensile strength of plstic vries with temperture; it decreses with incresing temperture over much smller temperture rnge.

3 .1 Understnding the Properties of Mterils 117 The modulus of elsticity (Mpsi) grph shows tht metls hve higher resistnce to deflection for short-term, intermittent, or continuous loding thn plstics. Metls hve better dimensionl stbility t elevted tempertures thn plstics. Since plstics deflect more thn metls under the sme loding, it is importnt tht metl nd plstic prts be loded using different techniques. Plstics require tht the lod be distributed in compression mode. The coefficient of liner therml expnsion grph shows tht incresing the temperture cuses more dimensionl chnges for plstics thn for metls. When plstics nd metls re used together nd re exposed to the sme tempertures, plstic prts become lrger thn metls; therefore, design compenstions should be provided to compenste dimensionl chnge in plstics. The therml conductivity grph shows tht metls re good conductors of het while plstics re excellent insultors. Despite their reltively low effective temperture rnge, plstics my be superior to metls s high temperture het shields for short exposures. A plstic prt exposed to rdint het source soon suffers surfce degrdtion. However, this het is not trnsmitted to the opposite surfce s rpidly s in metls. The electricl volume resistivity grph compres only the insultion mterils used in electricl pplictions, (metls re conductors). The dielectric strength grph shows the voltge grdient t which electricl filure or brekdown occurs s continuous rc; the higher the vlue the better the mteril. Plstics hve excellent electricl resistnce properties, while metls re conductors. Ferrous metls Nonferrous metls Thermosets Thermoplstics Rubber Mic lmintions Glss lmintions Thermosets Thermoplstics Rubber Mic lmintions Glss lmintions Thermosets Thermoplstics Therml conductivity (TU/hr/ft / F/in) x Electricl volume resistivity (Ohm-cm) Figure -1 (continued) Dielectric strength (Volt/.1 in) x Plstics Selection Guidelines More thn, thermoplstic grdes nd over 5, thermoset grdes hve been developed for the plstics industry. ecuse of the enormous diversity of plstic mterils, the selection of the best plstic mteril for given ppliction is reltively difficult nd time consuming, especilly for inexperienced plstic designers. Tble -1 provides comprison of plstics nd their properties. The tble includes the most widely used unreinforced, 3% GR thermoplstic, nd reinforced thermoset mterils; bsic mechnicl, therml nd electricl properties, nd process tempertures, indicting the process chrcteristics of the resins. Tble -1 should be used s preliminry plstic selection guide. The mteril properties listed in Tble -1 were obtined by the resin producers by testing molded brs using ASTM procedures under lbortory conditions. ecuse most pplictions re not flt brs, but complex configurtions, the ctul properties will be different from the published ASTM properties. The vlues given re only pproximte guides used to compre the vlues between resins for mteril selection nd for preliminry product design clcultions. To obtin precise properties for the new product design nd configurtion, prototype mold is required, molding the selected mterils, nd testing the performnce under ctul service conditions. This chpter provides detiled informtion for ll importnt plstics, their chemistry, chrcteristics, dvntges, limittions, nd pplictions. Severl plstic orgniztions, such s ASTM, Modern Plstics, D.A.T.A., Inc., Engineering Plstics, IDES Prospector nd ll the resin suppliers provide dt properties sheets.

4 118 Engineering Product Design Tble -1 Property Comprison for Selected Plstics Types of Polymers Specific Grvity Tensile 73 F (Mpsi) Tensile Yield (Kpsi) Notch Izod 73 F (ft-lb/in) Continue Expose Temperture ( F) Processing Temperture ( F) Flmmbility UL-94 Dielectric Strength (Vol/Mil) Dissiption Hz AS Unreinforced Acrylic Unreinforced Acetl Unreinforced HDPE Polyethylene Unreinforced PP Polypropylene Homo Unfilled PS Polystyrene Unfilled PVC Polyvinyl Chloride Rigid PC 3% Fiber Glss PPO 3% Fiber Glss No rek PT 3% Fiber Glss PET 3% Fiber Glss LCP 3% Fiber Glss HTN 3% Fiber 73 F 5% RH Nylon 6/6 33% 73 F & 5% RH PEI 3% Fiber Glss PPS - 3% Fiber Glss PSU 3% Fiber Glss DAP (TS) Fiber Glss (EP) Epoxy (TS) Fiber Glss (PF) Phenolic (TS) Fiber Glss (UP) Polyester (TS) Fiber Glss (PI) Polyimide (TS) Grphite Fiber H H H 56.5 H V H V H V H V1 V1 V H H 5V 5V V H V 5V 5V V1 H V1 5V 5V ,

5 .1 Understnding the Properties of Mterils 119 Designer Check List Generl Considertions Performnce requirements (structurl, loding cycle, esthetic, etc.) Multifunction design Product design for ssembly Structurl lod (sttic, dynmic, cyclic, impct, etc.) Product tolernce specifictions Life of product Resin selection bsed on performnce of similr pplictions nd end use Product design for ssembly process Qulity of product vs. process Secondry opertions Pckging nd shipping Environmentl Requirements End use temperture Time, wether, strin, nd stress crcks Others (chemicl, lubricnts, wter, humidity, pollution, gsoline, etc.) Design Fctors Type, frequency, direction of lods Working stress selected (tensile, compression, flexurl, combintion) Strin percentge selected Lod deformtion (tensile, sher, compression, flexurl, etc.) Tensile, flexurl, initil, secnt, yield modulus used (temperture, creep) Correlting the test results to end use environment conditions Sfety fctor Design product for efficient molding Economic Fctors Cost estimte of the new product Resin cost vs. molding performnce Number of mold cvities vs. size of mchine nd utomtic fst cycles Eliminte secondry opertions Redesign prt to simplify production Qulity Control Tests Required Tension Compression Flexurl Impct (drop weight, dyntup, etc.) Torsion, ftigue Creep (tension, flex, temperture) Chemicl resistnce Wether (outdoors or ccelerted) UL electricl clssifiction UL continuous service temperture UL temperture index Finl product UL pprovls Resin Processing Chrcteristics Viscosity nd crystlliztion Difficulties in molding the resin Melt nd mold temperture Sensitivity to therml degrdtion Directionl lyout of reinforcements Frozen stresses Mold shrinkge control Molding problems (flshing, voids, wrpge, short shots, brittleness, tolernces, surfce finishing, etc.) Mteril hndling Percentge of reground (runners nd rejected molded prts) llowed to mix with the virgin mteril Drying the virgin resin nd reground mteril. Prototype molding the product (resin behvior unknown) Appernce of Product Aesthetic product ppliction Dimensionl control, wrpge, etc. Color mtching, discolortion Surfce finishing Weld lines, sink mrks, flow lines Prting line flsh Gte type, size, number, loction Decortion

6 1 Engineering Product Design If the product informtion nd the qulity of dt vilble bout mteril hve not been developed by the resin supplier, the designer should develop check list by gthering ll the fcts relted to the ppliction. A typicl designer s check list hs been included here (Tble -). It my be used s guideline to develop specific check list for ny ppliction. All spects of the prt re covered, including the product end use requirements, the structurl considertions, the operting environment, the economics, nd the ppernce fctors. This informtion is provided for mking quick nlysis of the prt requirements, such s temperture, environment, product life expectncy, nd cycle nd rte of loding. Designing with plstics requires mximizing the performnce nd efficiency of the product nd the injection molding process. The following bsic principles should be dopted in designing plstic products. Design freedom is chieved using multifunctionl design concepts. When compring mterils tht stisfy the requirements, remember tht most metls hve greter strength thn plstics, nd tht ll plstic mteril properties re time, temperture, nd environment dependent. Metl design principles re very different from the concepts used in plstic prts design. Polymers re not substitutes for metls; in most designs the product geometry must be redesigned using plstic principles to be successful. We need to remember tht there re no bd thermoplstic mterils, only bd plstic pplictions.. Structurl Design of Thermoplstic Components Tensile stress, σ, (psi) E Modulus of elsticity P Stress limit O L Elstic rnge Strin, ε, (%) Figure - Stress-strin curve This section will present principles for structurl design of molded plstic prts. The only dt provided re wht is necessry to illustrte the type of informtion needed for nlysis of plstic design structures. The mechnicl properties described re the properties frequently used by designers of plstic components. Figure - shows two regions of the stress-strin curve. First, the region of low strin (O L) will be discussed. This region is known s the elstic rnge; it is pertinent to pplictions where minimum deformtion of the prt under lod is of prime concern. The second region of low stress (O P) is known s the stress limit, which is importnt when the specimen springs bck without deformtion. The following discussion of creep nd relxtion describes the effect of loding time on strength properties within the stress-strin curve. Specific ttention is pid to creep under constnt lod nd relxtion from fixed deformtion. The design methods present the recommended methods for using the mechnicl properties nd concepts for designing with plstics. Illustrtions re included to show how the equtions, originlly developed for metl designs, cn be modified. Designing within the viscoelstic modulus utilizes modified elstic design equtions. This method is normlly used when deformtion of the prt is of prime concern. Yield design uses design principles tht originte from the principles of plsticity. In this section, the yield stress is the controlling mteril

7 . Structurl Design of Thermoplstic Components 11 vrible. It is emphsized tht the mjor difference between metl nd plstic designs is the necessity of llowing for the time dependence of the mechnicl properties of polymeric mterils over the entire rnge of tempertures nd environmentl conditions tht the prt my encounter in use...1 Stress-Strin ehvior To understnd the response of the mteril, design engineers hve been using set of reltionships bsed on Hooke s lw, which sttes tht for n elstic mteril, the strin (deformtion) is proportionl to the stress (the force intensity). Rork nd Young, Timoshenko, nd others hve developed nlyses bsed on elstic behvior of mterils tht exhibit good pproximtion of simple elstic behvior over wide rnge of lods nd tempertures. For high stress levels nd repeted loding nd creep, more sophisticted nlyses hve been developed to del with these types of pplictions. Unfortuntely, Hooke s lw does not reflect ccurtely enough the stress-strin behvior of plstic prts nd it is poor guide to successful design, becuse plstics do not exhibit bsic elstic behvior. Plstics require tht even the simplest nlysis tke into ccount the effects of creep nd nonliner stressstrin reltionships. Time is introduced s n importnt vrible nd, becuse polymers re strongly influenced in their physicl properties by temperture, tht is nother importnt prmeter to be considered. In order to nlyze these effects, mthemticl models exhibiting the sme type of response to pplied forces s plstics re used. The elements tht re used in such n nlysis re spring, which represents elstic response becuse the deflection is proportionl to the pplied force, nd the dshpot, which is n enclosed cylinder nd piston combintion tht llows the fluid filling the cylinder to move from in front of the piston to behind the piston through controlled orifice. The retrded elstic response which occurs in plstic mterils is best represented s spring nd dshpot cting in prllel. The creep or cold flow, which occurs in plstics, is represented by dshpot. The combintion best representing the plstic structure would be spring nd dshpot in prllel combintion, in series with dshpot. The bsic elements nd the combintions re shown in Figure -3. One of the results of the viscoelstic response of polymers is to vry the reltionship between the stress nd strin, depending on the rte of stress ppliction. The stndrd test used to determine structurl properties for mny mterils is the nlysis of the stress-strin curve. Figure -4 shows the slope of the curve, which is the elstic constnt clled Young s modulus; the stress t which the slope of the curve devites from the stright line is referred to s the tensile strength; nd the stress t which the mteril fils by seprtion is clled the ultimte tensile strength. In the cse of viscoelstic behvior, the shpe of the curve will depend on the rte of loding or on the rte of strining, depending on the wy in which the test is performed. The modulus cn vry over rnge of three or four to one within the usul testing rnge nd the mteril cn exhibit ductile yielding t the lower strining rtes. The vlue of the tensile strength nd the ultimte strength cn frequently vry by 3 : 1 rtio. It is pprent tht, when tensile tests re done on plstics, the loding rtes must be specified to mke sure the dt hve ny mening t ll. It lso becomes cler G A G 1 1 G 1 A Model "A" 1 A Model "" A G Figure -3 Plstic resin structurl models, elstic nd plstic rnge Tensile stress, σ, (psi) Stress limit Elstic rnge E Young s modulus or modulus of elsticity Filure Figure -4 Young s modulus Strin, ε, (%) Ultimte tensile stress

8 1 Engineering Product Design Isochronous stress-strin curves Surfce t specific temperture tht such conventionl dt is essentilly useless for the design of plstic prts, unless the end use loding rtes hppen to be the sme s those of the test. In order to be useful, the tensile test would hve to be run over wide rnge of rtes nd the form in which the dt is best presented is three dimensionl plot of stress-strin nd time s illustrted in Figure -5. Stress Strin Log time Figure -5 Three-dimensionl grph, stress-strin-log time Creep curve.. Tensile Testing of Viscoelstic Mterils In this section we will ddress the internl effects of forces cting on structure. The thermoplstic components will no longer be considered to be perfectly rigid, such s in the sttic nlysis cses. Structurl design is concerned with the nlysis of mteril strength, such s the deformtions of vrious structures under vriety of lods. The simple tensile test is probbly the most populr method for chrcterizing metls nd so it is not surprising tht it is lso widely used for plstics. However, for plstics, the tensile test needs to be very crefully performed, becuse plstics, being viscoelstic, exhibit deformtions tht re very sensitive to such things s cross hed speed rte in tension testing, moisture, stress level, temperture, nd creep time. The stress-strin curves s shown in Figures -1 nd -11 illustrte n interesting phenomenon observed in some flexible plstics, such s thermoplstic elstomers. This behvior is known s the plstic rnge, cold drwing, or continuous elongtion of the specimen beyond the yield point without breking. It occurs becuse, t low cross hed speed rtes, the moleculr chins in the plstic hve time to lign themselves under the influence of the pplied stress. Therefore, the plstic specimen s moleculr chins re ble to lign t the sme rte t which the mteril it is being strined. The simplest cse to consider is the ppliction of stright tensile lod on test specimen of constnt cross section. The specimen is loded t both ends with n equl force pplied in opposite directions long the longitudinl xis nd through the centroid cross section of the tensile test specimen. Under the ction of the pplied tensile forces, internl resisting forces re set up within the tensile test specimen. The tensile test ssumes tht the forces re pplied through n imginry plne pssing long the middle of its length nd oriented perpendiculr to the longitudinl xis of the tensile test specimen. The mgnitude of these forces must be equl nd directed wy from the test specimen (tension loding) to mintin n equilibrium of these forces. Typicl tensile test equipment, including n extensometer, is shown in Figure -6. Some ssumptions re mde regrding the vrition of these distributed internl resisting forces within the specimen. ecuse the pplied tensile forces ct through the centroid, it is ssumed tht they re uniform cross the specimen s cross section. The lod distribution depends on the tensile test specimen geometry, dimensions, nd mnufcturing process. It lso depends on the crystlline moleculr structure of the polymer, the coupling gent used to reinforce the compound, nd the flow orienttion of the mteril reinforcement. However, to determine the mechnicl properties of polymer by performing either test in compression or tension, the cross hed speed rte, t which loding is pplied, hs significnt influence on the physicl properties obtined when running the tests t different loding rtes. Ductile mterils exhibit the gretest sensitivity of physicl property vritions t different cross hed speed loding rtes, wheres these effects re reduced nd sometimes negligible for brittle mterils.

9 . Structurl Design of Thermoplstic Components 13 Extensometer Figure -6 Tensile test equipment nd temperture chmber...1 Stress or Tensile Strength (σ) Insted of referring to the internl force cting on some smll element of the re, it is esier to use the rtio between the force cting over unit re of the cross section. The force per unit re is termed s the stress (σ) nd is expressed in units of force per unit re, e.g., lb/in (psi). If the forces pplied to the ends of the tensile test specimen re such tht the br is in tension, then the term stress or tensile strength (σ) condition cn be pplied to the specimen. It is essentil tht the forces re pplied through n imginry plne pssing through the centroid cross section re of the tensile test specimen.... Tensile Test Specimen The tensile test specimen is held in the grips of either n electriclly driven ger or hydrulic testing equipment. The electriclly driven ger testing equipment is commonly used in testing lbortories for pplying xil tension or compression lods. To stndrdize mteril testing procedures, the Americn Society for Testing Mterils (ASTM) hs issued stndrd specifictions nd procedures for testing vrious metllic, non-metllic, nd thermoplstic resins in tension nd compression tests. The ASTM test procedures for thermoplstic mterils cn be found in Chpter 11. Figure -7 shows tensile test specimen specified for plstic mterils. The dimensions shown re those specified by ASTM for tensile test specimens to fit the grips of the tensile test equipment. The elongtions of the tensile test specimen re mesured by mechnicl extensometer (see Figure -6), n internl guge (micro-processor tester), or by cementing n electric resistnce type strin guge to the surfce of the tensile test specimen. This resistnce strin guge consists of number of very fine wires oriented in the xil direction of the tensile test specimen. As the test specimen elongtes, the electricl resistnce of the wire chnges nd this chnge of resistnce is detected on Whetstone bridge nd interpreted s elongtion..75 inch 8.5 inch.5 inch.15inch Figure -7 Thermoplstic tensile test specimen

10 14 Engineering Product Design Stress-Strin Curves for Vrious Mterils Stress, σ, (psi) Y PL Stress, σ, (psi) Non ferrous lloys Y Stress, σ, (psi) PL Y Med. crbon steel Strin, ε, (%) 1 ε Strin, ε, (%) Reinforced resins Strin, ε, (%) Figure -8 Stress/strin curve for medium crbon steel Figure -11 Stress/strin curve for nonferrous lloys nd cst iron mterils Figure -14 Stress/strin curve for reinforced resins Stress, σ, (psi) PL Stress, σ, (psi) Stress, σ, (psi) PL Alloy steel Rubber / elstomers rittle resins Strin, ε, (%) Strin, ε, (%) Strin, ε, (%) Figure -9 Stress/strin curve for lloy steel Figure -1 Stress/strin curve for rubber or elstomeric mterils Figure -15 Stress/strin curve for brittle resins PL Stress, σ, (psi) Stress, σ, (psi) Y PL High crbon steel Unreinforced resins Strin, ε, (%) Strin, ε, (%) Figure -1 Stress/strin curve for high crbon steel Figure -13 Stress/strin curve for unreinforced resins

11 . Structurl Design of Thermoplstic Components Strin (ε) The elongtion over the tensile test specimen guge length is mesured for ny predetermined increment cused by the tensile lod. From these vlues the elongtion per unit length, clled strin nd denoted byε, my be found by dividing the totl elongtion L by the originl guge length L, i.e.,ε L / L. The strin is usully expressed in units of inch per inch nd consequently is dimensionless....4 Stress-Strin Curve As the tensile lod is grdully incresed t cross hed speed rte, the totl elongtion over the guge length nd the lod re mesured nd recorded continuously t ech increment of the lod until frcture of the specimen tkes plce. Knowing the originl cross sectionl re of the tensile specimen, the stress (σ), my be obtined for ny vlue of the tensile lod by pplying the following formul: Tensile Stress σ W / A where W denotes the tensile lod in pounds, nd A the originl cross sectionl re in squre inches. Hving obtined the numerous vlues of stress (σ) nd strin (ε), the test results re plotted with these quntities considered s ordinte nd bsciss, respectively. This is the tensile stress-strin curve or digrm of the mteril in tension. The stress-strin curve represents the mechnicl chrcteristics or behvior for ech type of mteril, therefore the stress-strin curves ssume widely differing geometries for vrious mterils. Figure -8 represents the stress-strin curve for medium crbon steel, Figure -9 the curve for n lloy steel, Figure -1 the curve for high crbon steel, Figure -11 the curve for nonferrous lloys nd cst iron mterils, nd Figure -1 the curve for rubber or elstomeric mterils. Tests conducted t room temperture using ASTM recommended proportionl limits showed tht polyethylene resin, PP copolymer resin, TPE resins, cetl resin, nd unreinforced nylon resin (t 5% reltive humidity) re mterils tht yield grdully until brek s shown in Figure -13. Reinforced nylon resin (t 5% reltive humidity), PC glss reinforced resin, nd other compounded polymers tht hve limited elongtion chrcteristics yield curve s shown in Figure -14. Acrylic resin, PET glss reinforced resin, PT glss reinforced resin, LCP, PF, PAI, PEI, PEAK, dry s molded nylon glss reinforced resins nd most brittle compounded resins usully brek before yielding occurs, s shown in Figure Hooke s Lw For ny mteril hving stress-strin curve of the form shown in Figure -16, the reltion between stress nd strin is liner for comprtively smll vlues of the strin. This liner reltion between elongtion nd tensile stress ws first noticed by Sir Robert Hooke in 1678 nd is clled Hooke s lw. This initil liner rnge of ction of the mteril is described by the following formul: or Stress (σ) Modulus of Elsticity (E) Strin (ε) Strin (ε) σ / E where E (Modulus of Elsticity) denotes the slope or the stright line -PL (origin to the proportionl limit) s shown in the stress-strin curve Figure -16.

12 .16 Flt Circulr Pltes 1 Tble -5 Flt Circulr Plte Equtions, Prt I W Concentrted lod (lb); w Unit lod (psi); M Moment (in-lb/in); Deflection (in);θ Chnge in slope (rdins); E Modulus of elsticity (psi); H Deflection fctor (in.);υ Poisson s rtio;σ Stress (psi); t Wll thickness (in); Outer rdius (in); b Inner rdius (in); d Shft rdius; r Rdius of lod (in); K Plte constnt Cse Type Stress nd Deflection Equtions (Constnt Thickness) Concentrte Center Lod Edge Simply Supported W y 3 W (1 + υ) 1 1 υ r σ + log + π t υ 1 r υ 4 3 W (1 υ)(3 + υ) 4π E t Mx. 3 Uniform Distribute Lod Edge Simply Supported edge simply supported 3 w (3 + υ) w y σmx. 8 t 4 3 w (1 υ)(5 + υ) 16 E t Mx. 3 For > r Concentrted Center Lod Outer Edge Fixed W y σ 3 W (1 + υ) r log + π t r 4 Mx. 3 W (1 υ ) 4π E t Mx. 3 Uniformly Distributed Lod Outer Edge Fixed w y σ 3 w 4 t Mx. 4 3 w (1 υ ) 16 E t Mx w (1 υ ) H 16 E t Mx. 3 For thicker flt circulr pltes hving (t /.1), multiply the deflection eqution by the constnt (H), where *H (t / ). Centrl Couple Outer Edge Simply Supported M.49 K ( d +.7 ) d σ 3 M ( d) 1 + ( υ + 1) log 4π d t K Mx. Centrl Couple Outer Edge Fixed M d.1 K ( d +.8 ) σ 3 M (.45 d) 1 + ( υ + 1) log 4π d t.45 K Mx. Rdil Center Lod Edge Simply Supported W b y σ Wυ υ 1 log + 1 π t ( + b ) b μ Mx Wυ 1 ( b ) b + 1 υ υ υ + log 4π E t 1 1 b + 1 ( b ) υ υ 1 Mx. 3

13 Engineering Product Design Tble -5 Flt Circulr Plte Equtions, Prt II W Concentrted lod (lb); w Unit lod (psi); M Moment (in-lb); Deflection (in);θ Angulr chnge (rd.); Q sher (lb/in); E Modulus (psi);υ Poisson s rtio;σ 6M/t (psi); t Wll thickness (in); Outer rdius (in); r Rdius of lod (in); D E t 3 / 1 (1 ν ); N Equivlent rdius (in); K, C, L, G Constnts (rtio-dependent) Cse Type oundry Vlues Specil Cses Outer nd Inner Edge Simply Supported; Centrl Rdil Lod W r O Outer & Inner Edges Fixed; Chnge in Slope O r O Uniform Distributed Lod; Edge Simply Supported r O w, M,, M b rb r Kθ W b θb D Q K W b Qb θ θ W b C4 + Qb C6 L6 D D b W ro Q Qb, θ,, θ b b KMrbθo D b Mrb ; Q Qb KQbθo D Qb ; Mx. Koθ D Mr Mrb C8 + Qb C9 + θo L7, Mr ; MC w G17 θ 4 W G17 C G11 D 1 + υ w ( ) 8 D (1 + υ) ro b / r o / K Mx Kθ Kθ b K Mrb K Mro K Qb b / r o / K o K Mrb K Mr K Qb r o / K C Kθ K MC w (3 + υ) Q ( ro ); If ro, G11.15, G14.6, G w w w (5 + υ) w (3 + υ) w L T G11; L Tθ G14 ; C ; MC ; θ D D 64 D (1 + υ) 16 8 D (1 + υ) Liner Increse Lod; Edge Simply Supported w r O, Mr ; MC w G18 4 w G18 C G1 D 1 + υ w Q ( ro ro ) 6 θ r o / w G18 G15 ; If ro, G1.4, G15., G18 K C Kθ K MC (4 + υ) D 1 + υ o (6 υ) (4 υ) 1; C ; C ; θ o υ w r w + w + L T w G M D r 15 D (1 + ) D (1 + υ) Centrl Circulr Lod; Edge Simply Supported W r r O W (3 + υ) W r 1 For r > ro ; ( r ) r ln ; θ ln 16 π D + (1 + υ) r 4 π D (1 + υ) r W ( ) r 4 (1 ) ln (1 ) r N M + υ + υ ; N 1.6 r o + t.67 t; If ro <.5 t 16π r r W N or N r, If r >.5 t; M 4 (1 + υ) ln + (1 υ) 4 16π r r o o t W (3 + υ) W W t r ; Mx. ; θmx. ; MMx. (1 + υ) ln π D (1 + υ) 4 π D (1 + υ) 4π N

14 .16 Flt Circulr Pltes 3 esides the usul lodings, Tble.5 Prt II lso includes severl loding cses tht my be described best s externlly pplied conditions tht force lck of fltness into the flt circulr pltes. The first time we look t Tble.5, Prt II it ppers to be formidble tsk to clculte the strength of these structures. However, when we consider the number of cses it is possible to present in limited spce, the reson for this method of presenttion becomes cler. With creful inspection, we find tht the constnts nd functions with subscripts re the sme except for the chnge in vribles. In Tble.5, Prt II, the tbulted vlues in the Specil Cses re listed for the preceding functions for the most frequently used denomintor vlues of the vrible rtios, such s b / nd r /. Exmple -41 A flt circulr plte is mde of nylon 6/6 with 33% fiber glss reinforcement t 73 F nd 5% reltive humidity. The rdius is 3. in with wll thickness of.5 in. The plte is simply supported round its edge nd it is loded with 5. lb t the center. The lod is distributed through round re of.15 in rdius. Determine the mximum bending stress t the surfce of the plte nd the mximum deflection t the center of the plte. Solution This flt circulr plte nd loding re covered in Tble.5, Prt I, cse lod t center with the outer edge simply supported. The digrm nd equtions in Figure -96 were obtined from this tble: t.5 in, w 5 lb, 3. in, r.15 in, E 9, psi,υ.39,σ 18, psi σ 3 W (1 + υ) 1 1 υ r Mx. log π t + υ + 1 r 1 + υ 4 1,794 psi 3 5 (1 +.39) log W Figure -96 Flt circulr plte, concentrted center lod, nd simply supported edge 3 W (1 υ) (3 + υ) (1.39) (3 +.39) 4π E t ,.5 Mx in Exmple -4 A thick flt circulr plte is mde of nylon 6/6 with 33% fiber glss reinforcement t 73 F nd 5% reltive humidity with rdius of 4. in nd uniform wll thickness of.5 in. The plte s outer edge is fixed nd it is uniformly loded long the round re of plte with. lb/in. Determine the mximum bending stress t the surfce of the plte nd the mximum deflection t the center of the plte.

15 4 Engineering Product Design w Figure -97 Flt circulr plte, uniformly distributed lod, nd fixed edge Solution This thick flt circulr plte nd type of loding is presented in Tble.5, Prt I, cse Uniformly Distributed Lod with the Outer Edge Fixed. The digrm nd equtions in Figure -97 were obtined from the tble. ecuse this exmple cse dels with thick plte, we need to investigte if the thickness / rdius rtio is greter thn.1 to modify the mximum deflection by multiplying the vlue by the constnt (H). t.5 in, w psi, 4. in, E 9, psi, υ.39,σ 18, psi For thicker flt circulr pltes with rtio t / >.1, multiply the deflection eqution by the constnt (H), where H (t / ). t > H ( t / ) (.5/4.) 1.89 σ 3 w ,3. psi π t Mx w (1 υ ) 3 4. (1.39 ).7 in E t 16 9,.5 H x y in Mx. r O w Exmple -43 A flt circulr plte, mde of cetl homopolymer, hs wll thickness of.187 in nd 5. in outside dimeter, nd is simply supported with uniformly distributed lod of 6. psi. Clculte the mximum deflection in the center, the mximum stress, nd the deflection eqution for Figure -98. This flt circulr plte nd type of loding is presented in Tble.5, Prt II, cse Uniformly Distributed Lod Edge Simply Supported. First, we need to determine the mximum moment, the bending stress, the plte constnt, nd the deflection cused by the lod. Second, we need to clculte the totl deflection of the plte cused by the lod, the moment, nd the loding constnt. Finlly, we need to check the deflection t the outer edge. t.187 in, w 6. psi,.5 in, r, E 41, psi,υ.35,σ 1, psi Figure -98 Flt circulr plte, uniformly distributed lod with simply supported edge M σ Mx. w (3 + υ) 6..5 (3 +.35) MCenter 7.85 lb-in M , psi t.187 Mx.

16 .16 Flt Circulr Pltes E t 41,.187 D (1 υ ) 1 (1.35 ) C 4 4 w (5 + υ) 6..5 (5 +.35).565 in 64 D (1 + υ) (1 +.35) The totl deflection eqution for the flt circulr plte is: MC y C + + L Ty, where for this cse D (1 + υ) L T y w D 4 G 11 Where the constnt G 11.15, when r Checking the deflection t the outer edge, when.5 in Exmple -44 A flt circulr plte is mde of cetl homopolymer with wll thickness of.15 in nd 4. in outside dimeter. It is mounted in fixture to produce sudden chnge in slope in the rdil direction of.5 rdint t rdius of.75 in. It is then clmped between two flt fixtures s shown in Figure -99. Clculte the mximum bending stress. This is n exmple of forcing known chnge in slope into flt circulr plte, clmped (fixed) t both inner nd outer edges. This flt circulr plte nd type of loding is presented in Tble.5, Prt II, cse Outer nd Inner Edge Fixed nd Chnge in Slope, where:θ.5, b /.1, r /.5 nd Poisson s rtio ofυ.35. t.15 in, 1.5 in, b.15 in, r.75 in, θ.5 rd.,θ b. rd., b. in, E 41, psi, υ.35,σ 1, psi 3 3 E t 41,.15 D (1 υ ) 1 (1.35 ) θ O r O 4. di..15 M Q b rb K Mrb θ D lb-in. 1.5 KQb θ D lb/in r. 1.5 r..5 rd..75 r. Figure -99 Flt circulr plte hving chnge in slope with both outer nd inner edges fixed

17 6 Engineering Product Design D Mr Mrb C8 + Qb C9 + θ L C + (.154) C + L σ M rb Mx ,996.8 psi t.15 Mx. K yθ r in Exmple -45 A flt circulr plte, mde of cetl homopolymer, hs wll thickness of.5 in nd 5. in outside dimeter, it is simply supported t the outer edge nd subjected to two types of lods. One center lod provides uniform pressure over dimeter of.65 in. The other is xis-symmetriclly loded with distributed lod tht increses linerly from the center to the outside rdius r O 1. in;, this lod hs vlue of 1. psi t the outer edge. Clculte the mximum bending stress. This exmple requires nlyzing two different cses nd to superposition the results. The first cse is the liner increse of the distributed lod with simply outer edge supported (Figure -1), the second cse is the centrl circulr uniform lod with simply supported outer edge (Figure -11). oth cses re presented in Tble.5, Prt II. t.5 in,.5 in, r 1 1. in, r.31 in, E 41, psi,υ.35,σ 1, psi From the specil cse dt, the following vrible rtios re obtined: w r O1 r 1 / 1 /.5.4, K y C.164, K θ.78, K MC.449 Figure -1 First cse: Liner decresing distributed lod nd edge simply supported 3 3 E t 41,.5 D (1 υ ) 1 (1.35 ) 4 4 w K yc.15 in D P r M K w lb-in. Mx. MC P (3 + υ) P.5 (3 +.35).15 in 16 π D (1 + υ) 16 π (1 +.35) P.76 lb. r O Figure -11 Second cse: Center uniformly circulr lod nd edge simply supported The second moment component is clculted by using the equtions provided in Tble.5, Prt II, cse Centrl Circulr Loding nd Simply Outer Edge Supported.

18 .17 Torsion Structurl Anlysis 7 N 1.6 r + t.675 t in M Mx. P.76.5 (1 υ) ln 1 (1.35) ln 1 4π N 4π lb-in. σ 6 M 6 ( ) psi t.5 Mx..17 Torsion Structurl Anlysis A br is rigidly clmped t one end nd twisted t the other end by torque T F d, pplied in plne perpendiculr to the xis. Plne sections remin plne nd rdii remin stright. There is t ny point sher stress (τ) on the plne of the section; the mgnitude of this stress is proportionl to the distnce from the center of the section nd its direction is perpendiculr to the rdius drwn through the point. The deformtion nd stresses re shown in Figure -1. In ddition to these deformtions nd sher stresses, there re the longitudinl strin nd stress. The longitudinl strin is reduced while the stress is in tension on the outside nd blncing compression stress is exerted on the inside. F d Figure -1 Deformtion nd stress under torque L T F x d Assumptions The torsion equtions re bsed on the following ssumptions: The br is stright, of uniform circulr cross section (solid or tubing), nd of homogeneous isotropic mteril. The br is loded only by equl nd opposite twisting couples, which re pplied t its ends in norml direction to its xis. The br is not stressed beyond the elstic limit of the mteril. Angle of Twist (θ) If shft of length (L) is subjected to constnt twisting moment (T) long its length, then θ is the ngle through which only one end of the br will be twisted. Twisting Moment (T) The twisting moment T for ny section long the br is defined to be the lgebric sum of the moments of the pplied couples tht lie to one side of the section in question. Shering Strin If br is mrked on the surfce (unloded), then fter the twisting moment (T) hs been pplied, this line moves s shown in Figure -1. The ngle (θ) is

19 8 Engineering Product Design mesured in rdins; the finl nd originl position of the genertor is defined s the shering strin t the surfce of the br. Shering Stress (τ) For solid circulr cross section br, let T Twisting moment; L Length of the br; r Rdius; J Polr moment of inerti;τ Sher stress;θ Angle of twist (rdins); G Modulus of rigidity. Then: θ ( T L)/( G J) ; τ Mx. ( T r )/ J 4 y substituting for J ( π r )/ in the eqution bove for solid circulr cross section with rdius r, the following equtions re obtined: 4 θ ( T L)/( π r G) ; τ 3 Mx. T π r ( )/( ) For circulr tube cross section with outer rdius r nd inner rdius r i : 4 4 i θ ( T L)/ π ( r r ) G] ; τ 4 4 Mx. T r π r ri ( )/[ ( )] The torsionl stiffness of the br cn be expressed by the generl eqution: θ (T L) / (G K), where K is fctor dependent on the br cross section. For cross section brs, the fctor K is equivlent to the polr moment of inerti J. In Tble -6, the equtions for the fctor K nd for the mximum sher stress (τ Mx. ) for vriety of cross section brs re given. Exmple -46 Compre the strength nd stiffness of circulr injection molded tube mde of plstic mteril, 1. in outside dimeter nd.187 in wll thickness, versus n extruded solid circulr br of the sme mteril with the sme dimeter. The strengths of both cross sections will be compred by using the twisting moments (T) required to produce the sme sher stress. The stiffness will be compred by using the vlues of fctor (K) for both cross sections. For the circulr tube br: i K π ( r r )/ ( )/.83 in i τ T τπ ( r r )/( r ) ( )/(.5) τ.166 lb-in. For the solid circulr br: K T π r / /.98 in 3 3 ( τπ r )/ τ / τ.196 lb-in. The solid circulr cross section br is therefore 1.18 times s stiff s the circulr tube cross section br nd 1.18 times s strong.

20 .17 Torsion Structurl Anlysis 9 Tble -6 Torsion Equtions Cross section Solid circle Constnt K in T L θ K G Sher stress mx. r O K 4 π ro τmx. 3 π ro T Circulr tube r O K 4 4 O ri π ( r ) τ T r O Mx. 4 4 π ro ri ( ) r i Solid ellipse r S K 3 3 π rl rs rl + rs τ T Mx. π rl rs r L Solid squre 4 K.146 τ Mx. 3 T.8 Solid rectngle b K b b 1 b 4 τ T (3 b ) b Mx. θ Angle of twist (rdins); T Twisting moment (lb-in);τ Sher stress (psi); G Modulus of rigidity (psi); J Polr moment of inerti (in 4 ); K Constnt equivlent to J (in 4 ); r o Outer rdius (in); r i Inner rdius (in); r S Ellipticl short rdius (in); r L Ellipticl lrge rdius (in); Height (in); b Width (in).

21 11 3 Structurl Designs for Thermoplstics Poor design 3.1 Uniform nd Symmetricl Wll Thickness The ultimte design rule for injection molding thermoplstic products is to ensure tht the wll thickness is uniform nd symmetricl. Non-uniform nd/or hevy wll thicknesses cn cuse serious wrpge nd dimensionl control problems in the injection molded products. Hevy wll sections cuse not only internl shrinkge, voids, nd surfce sink mrks, but lso nonuniform shrinkge resulting in poor dimensionl control nd wrpge problems. Figure 3-1 shows poor cross section design of perpendiculr corner wlls tht cuses molding problems, such s differentil shrinkge, wrpge (concve) of both wlls, nd internl voids in the corner of the thicker wll. The lst two designs re recommended to void these molding problems. Figure 3- shows hevy wll cross section design tht could cuse molding problems nd the recommended design using thin wll nd proportionl ribs. Figure 3-3 shows nonuniform wll section tht should be replced with thin uniform wll hving the sme strength of the originl hevy wll section. Figure 3-4 shows nother poor nd the recommended uniform wll design. Figures 3-5 nd 3-6 show cross sections of two nonuniform wll designs nd the recommended designs with uniform wll thickness to void wrpge, internl voids, long molding cycles, nd surfce sink mrks. Wrpge Molding problems Good design R. r. Shrp corner Voids Figure 3-1 Perpendiculr wlls, end corner designs Good design r. Set Poor design Good design Figure 3- Hevy wll vs. thin uniform ribbed wll designs Poor design Good design Figure 3-5 Nonuniform wll vs. thin uniform wll designs Poor design Good design Figure 3-3 Nonuniform wll vs. thin uniform wll designs Poor design Good design Poor design Good design Figure 3-4 Nonuniform wll vs. thin uniform wll designs Figure 3-6 Nonuniform wll vs. thin uniform wll designs