2.5 - Case studies. Outline. Materials for oars Materials for flywheel Materials for spark plug insulators Air cylinders for trucks

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1 - Ashb Methd.5 - ase studies Outline Materials fr ars Materials fr flwheel Materials fr spark plug insulatrs Air clinders fr trucks Resurces: M. F. Ashb, Materials Selectin in Mechanical Design Butterwrth Heineann, 1999 hapter 6 The abridge Material Selectr (ES) sftware -- Granta Design (

S specified st within reasn Tughness adequate rss-sectin area

2 Materials fr ars Materials fr ars Specificatin Functin Objectives nstraints Free variables Oar: light, stiff bea Miniu weight Stiffness S specified st within reasn Tughness adequate rss-sectin area Material Oars are stiffness-liited, iniu weight, designs Multiple cnstraints prble

3 Materials fr ars Functin Bea (slid square sectin). b F Objective nstraint Free variables 1 S L = Miniise ass,, where: = AL = b L Stiffness f the bea S: EI S = 3 L I is the secnd ent f area: 4 b I= 1 Material chice. Edge length b. bining the equatins gives: 5 1/ 1/ E b = ass A = area L = length = densit b = edge length S = stiffness I = secnd ent f area E = Yungs Mdulus hse aterials with sallest L 1/ E Materials fr ars Specificatin Functin Objectives nstraints Free variables Oar: light, stiff bea Miniu weight Stiffness S specified st within reasn Tughness adequate rss-sectin area Material Oars are stiffness-liited, iniu weight, designs Multiple cnstraints prble Priar cnstraint Perfrance axiizing criteria Material liits, set b cnstraints Fracture tughness K 10 MPa. lc 1/ Material index, set b bjective Miniise M = 1 / E Densit Mdulus

Search area Materials fr ars -- hard cp chart 1 3 4 M

$(and txicit) rules it ut 4 eraics: But fracture$ tughness inadequate Oars: real life Wd: Sitka spruce,

4 Search area Materials fr ars -- hard cp chart M = 1/ E The selectin 1 Wd: heap, light, but variable FRP: The best chice, re cntrl f design 3 Berlliu: cst (and txicit) rules it ut 4 eraics: But fracture tughness inadequate Oars: real life Wd: Sitka spruce, quartered and lainated FRP: Tailred t rwer s specificatin Flwheels

5 Real flwheel -- filaent-wund GFRP ase Burst shield Rtr Specificatin fr a flwheel Specificatin Functin Flwheel Objectives nstraints Free variables Maxiu energ/weight Must nt disintegrate st within reasn Fr. Tughness adequate Material Multiple cnstraints prble

Material index and cnstraints fr flwheels Maxiise energ/unit weight at axiu velcit Angular velcit Ment f inertia 4 Energ Ιω π R t U = Ι = Mass = πr t Densit Must nt fail ( 3 + ν ) = R ω 8 Strength

6 Material index and cnstraints fr flwheels Maxiise energ/unit weight at axiu velcit Angular velcit Ment f inertia 4 Energ Ιω π R t U = Ι = Mass = πr t Densit Must nt fail ( 3 + ν ) = R ω 8 Strength (1) () (3) Energ/ass U ( 3 + ν ) 8 1 (4) Maxiise M = Additinal cnstraint: Fracture tughness > 15 MPa. 1/ Material fr flwheels 1 M= The selectin 1 eraics: But fracture tughness inadequate FRP, GFRP: The best chice

7 Spark-plug insulatrs Specificatin Functin Objectives nstraints Free variables Spark-plug insulatr Miniise aterial cst Gd electrical insulatr Breakdwn V > 0 MV/ Tlerate tep. > 600 Resist theral shck f 100 Material Insulatr Bd shell entral electrde Multiple cnstraints prble Analsis fr spark plug insulatrs nstraints: R > μh.c V ax > 0 MV/ T ax > 600 Teperature change Theral Strain ε = α ΔT (1) T-expansin cefficient Yung s dulus Stress: = E ε () Elastic liit Insulatr Bd shell Fracture when: = el in tensin (3) bining (1) t (3) gives allwable T-shck: entral electrde ΔT ax = el Eα Ipse ΔT > 100 as a cnstraint, then iniise aterial cst

Materials fr spark-plug insulatrs 10000 Search regin Silica Theral shck - cst The selectin: aluina Theral shck resistance,

8 Materials fr spark-plug insulatrs Search regin Silica Theral shck - cst The selectin: aluina Theral shck resistance, ΔT () Theral shck resistance () Aluinas Glass eraics Silicn Nitrides Aluiniu Nitrides Additinal cnstraints: Electrical resistivit > μh.c Breakdwn ptential > 0 MV/ Maxiu service teperature > 873 K Price (tpical) (GBP/kg) Apprxiate aterial cst ($/kg) ase stud: Air clinders fr trucks Design gal: lighter, cheap air clinders fr trucks pressed air tank

Design requireents fr the air clinder Specificatin t Functin Pressure vessel Pressure p R Objectives nstraints Miniise ass Miniise cst Diensins L, R, pressure p, given Must nt crrde in water r il

9 Design requireents fr the air clinder Specificatin t Functin Pressure vessel Pressure p R Objectives nstraints Miniise ass Miniise cst Diensins L, R, pressure p, given Must nt crrde in water r il Wrking teperature -50 t Safet: ust nt fail b ielding Adequate tughness: K 1c > 15 MPa. 1/ L R = radius L = length = densit p = pressure t = wall thickness Free variables Wall thickness, t; hice f aterial Perfrance etrics fr the air clinder Thin-walled pressure vessels are treated as ebranes. The apprxiatin is reasnable when t < b/4 The stresses in the wall d nt var significantl with radial distance, r z r θ θ p bl pb = = tl t pe + pi p r = = p πb pb z = = π bt t b b t < > 4 4 t

10 Perfrance etrics fr the air clinder Vlue f aterial in clinder wall t = ( πrl t + 4πR t) Objective 1 nstraint Metric 1 pr = < t Eliinate t t give: = πr L S f ( 1+ Q) R = π RL t1 + L Aspect rati Q psf Pressure p L R R = radius L = length = densit p = pressure t = wall thickness = ield strength S f = safet factr Q = aspect rati R/L Objective Metric = = πr L ( 1+ Q) psf Substitutin: Relative perfrance etrics This is a prble f substitutin. The tank is currentl ade f a plain carbn steel. The ass and cst f a tank ade fr an alternative aterial M, differs (fr the sae strength) fr ne ade f M b the factrs =., =.,, Fr plain carbn steel /, = 0.03 and / 0.0,, = Explre the trade-ff between and

11 Trade-ff plt Lead alls Additinal cnstraints: Mass relative Densit t plain / Elastic carbn liit steel, / Mild steel High- steel Lw all steel Trade-ff surface Al-alls Mg-alls Zn-alls u-alls Ni-alls K 1c >15 MPa. 1/ T ax > 373 K T in < 3 K Water: gd + Organics: gd + Al-Si psite GFRP FRP Ti-alls Price * Densit / Elastic liit st relative t plain carbn steel, / Trade-ff plt The fur sectrs f a trade-ff plt fr substitutin Lead alls Mass relative Densit t plain / Elastic carbn liit steel, / Mild steel B. heaper but heavier High- steel Lw all steel Zn-alls Al-alls Mg-alls A. Better b Al-Si psite bth etrics GFRP D. Wrse b bth etrics FRP u-alls Ni-alls. Lighter but re expensive Ti-alls Price * Densit / Elastic liit st relative t plain carbn steel, / High- steel, lw all steel and Al-alls all ffer reductin in ass and cst

12 Prble slutin Selected aterial M (r aterials) t substitute carbn steel,, Mass and cst f a tank ade fr the alternative aterial M Free variable (thickness) t =,. =,, /, = 0.0 /,, = f S t pr < =

Lecture 7 Further Development of Theory and Applications

Lecture 7 Further Development of Theory and Applications P4 Stress and Strain Dr. A.B. Zavatsk HT08 Lecture 7 Further Develpment f Ther and Applicatins Hke s law fr plane stress. Relatinship between the elastic cnstants. lume change and bulk mdulus. Spherical