3.6.5 · D1Yield stress, ultimate stress — material behavior
Jab aap ek solid rod ko kheenchte ho, woh stretch hoti hai — aur kitni stretch hoti hai kitna kheenchne par, yahi poora subject hai. Yeh page har woh letter aur picture build karta hai jo aapko woh story padhne ke liye chahiye: ek axis par force per area , doosri par fractional stretch , aur do danger lines (permanent bend, phir break) us par kheenchi hui.
Stress–strain curve padhne se pehle aapko uske har symbol ki poori samajh honi chahiye. Hum unhe ek ek karke build karte hain, har ek ko plain-words meaning, ek picture, aur ek reason ke saath justify karte hue ki topic uske bina kaam nahi kar sakta. Neeche kuch bhi yeh assume nahi karta ki aapne yeh pehle dekha hai.
Sab kuch ek single object se shuru hota hai: ek seedhi metal rod jise dono ends se kheencha ja raha hai. Figure dekhein — yeh woh picture hai jis par is page ka har symbol tika hua hai.
Definition Chaar cheezein jo aap point kar sakte hain
Rod ki ek original length L 0 A 0 Aap ise ek force F
Yeh thodi si matra Δ L lamba ho jaata hai (Greek letter delta, Δ
"Cross-sectional area" = cut face ka area, pull ke perpendicular. Radius r A 0 = π r 2 A 0 = width × thickness
Yahan se kyun shuru karein? Kyunki poora topic isi ek experiment par measure kiye gaye do numbers hai. Agar rod clear hai, toh har symbol us par sirf ek label hai.
Force ek push ya pull hai. Iska unit newton (N
Picture: Figure 1 mein amber arrows. Lamba arrow = harder pull = bada F
Topic ko kyun chahiye: F cause hai. Rod isliye stretch hoti hai kyunki aap use kheenchte ho. Lekin — aur yahi reason hai ki agla symbol exist karta hai — force akela aapko nahi batata ki rod danger mein hai ya nahi.
Definition Original cross-sectional areaA 0 kheenchne se pehle measure kiya gaya (chota subscript 0 m 2
Picture: Figure 2 mein shaded disc — woh face jo aapko dikhega agar aap rod ko cleanly kaat dein.
Intuition Area utna hi important kyun hai jitna forceDo ropes imagine karein, moti aur patli, same force se kheenchi gayi. Patli wali tootne ke zyada karib hai. Same pull "kam material mein concentrate" ho raha hai. Woh word concentration exactly wahi hai jo agla symbol capture karta hai.
Ab hum pichle dono combine karte hain. Greek letter σ
Definition Stress (engineering stress)Stress = force divided by original area.
σ = A 0 F pascal (Pa N/m 2
Common mistake Pascals bahut chhote hote hain — bade prefixes expect kareinEk pascal bahut chota stress hai. Real metals millions of pascals par fail karte hain, isliye topic yeh use karta hai:
kilopascal 1 kPa = 1 0 3 Pa
megapascal 1 MPa = 1 0 6 Pa
gigapascal 1 GPa = 1 0 9 Pa
Parent note ka "80 MPa 80 × 1 0 6
Topic ko kyun chahiye: σ σ Stress and strain fundamentals dekhein.
Strain (Greek letter ε ε = L 0 Δ L koi units nahi — yeh ek length divided by ek length hai. 0.001 0.1%
Picture: Figure 1 mein, Δ L ε poori rod ke comparison mein kitna bada hai?"
Intuition Fractional kyun, absolute kyun nahi10 mm bolt par 1 mm stretch bahut bada hai; wahi 1 mm ek 10 m beam par kuch bhi nahi hai. L 0 material describe karta hai, na ki sample ka size . Isliye same metal ki do alag-alag size ki rods ek hi strain-at-yield share karti hain.
Ab hamare paas dono axes hain: σ ε
Definition Young's modulusYoung's modulus E σ = E ε ε E GPa
Common mistake Stiff ka matlab strong nahiE σ y σ u alag ideas hain. Stiff material elastic stretch resist karta hai; strong wala breaking resist karta hai. Young's modulus and elasticity dekhein.
Yeh sirf σ
Definition Yield aur ultimate stress
Yield stress σ y y Ultimate tensile stress σ u u
Picture: Figure 3 par, σ y σ u
Intuition Do numbers kyun, ek kyun nahiσ y "part ab permanently bent hai — precision work ke liye kharab ho gaya." σ u "part tootne wala hai." Spacecraft design real stress ko dono ke neeche rakhhta hai, aur safety ke saath. Yeh Factor of safety and margins aur Material selection for spacecraft ko feed karta hai.
Do chhote notation bits har jagah milte hain; inhe aapko trip nahi karne chahiye.
Definition Chhoti print padhna
Δ "us quantity mein change." Toh Δ L = L after − L before Ek subscript 0 A 0 L 0 "original, undeformed value" — kisi bhi kheenchai se pehle measure ki gayi.
Topic ko kyun chahiye: poora subject before aur after compare karta hai. 0 starting area use karte hain (yahi choice ise "engineering" stress banati hai na ki "true" stress).
Aakhri symbols metal ki physics nahi hain; yeh hain ki engineers numbers ko kaise use karte hain.
Definition Safety numbers
Factor of safety FoS Margin of safety MoS MoS ≥ 0 FoS = σ a pp σ allow , MoS = F o S r e q ⋅ σ a pp σ allow − 1
Intuition Ratio kyun aur one subtract kyun kareinEk ratio answer karta hai "multiples mein kitna headroom hai?" — 2 ka factor matlab "humein jitni zaroorat hai usse do guna." One subtract karne se "humara required strength ka 1.27× hai" ban jaata hai "+ 0.27 Factor of safety and margins mein fully rakhte hain, aur jo loads σ a pp Structural load cases and launch loads se aate hain.
Stress sigma equals F over A0
Strain epsilon equals delta L over L0
Young modulus E is the slope
Design margins FoS and MoS
Material behavior for spacecraft
Ise top to bottom padhein: force aur area stress banate hain; length-change aur length strain banate hain; yeh dono axes plus slope E σ y σ u parent topic actually kya hai.
Self-test: right side cover karein aur reveal se pehle har ek answer dein.
Symbol F Force (ek push/pull); unit newton, N
A 0 0 Cut face ka original (undeformed) cross-sectional area; 0
Stress ki definition aur iska unit likhein. σ = F / A 0 Pa = N/m 2
1 MPa 1 0 6
Strain ki definition aur iske units likhein. ε = Δ L / L 0
Kisi quantity ke aage Δ "Change in" — after value minus before value.
Young's modulus E Stress–strain graph ke straight (elastic) part ka slope; σ = E ε
Kya zyada stiff material (bada E Nahi — E σ y σ u
Curve par σ y Woh stress jahan permanent deformation shuru hoti hai — line straight track chhod deti hai.
Curve par σ u Peak — woh maximum engineering stress jo material sustain karta hai.
FoS Allowable stress applied stress se kitni baar bada hai (ek dimensionless ratio).
MoS ≥ 0 Part pass ho jaata hai — woh required safety factor ke saath survive karta hai.
Mnemonic Do axes, do dangersAcross = strain (kitna stretch hua), upar = stress (kitna hard, per area). Stress axis par do danger lines hain yield (permanently bend ho jaata hai) phir ultimate (toot jaata hai).
