YEH do design dominate kyun karte hain: Yield batata hai jab part permanently kharaab ho jaata hai (ek bent strut spec par wapas nahi aayega). Ultimate batata hai jab part khatam ho jaata hai. Structures ko dono survive karne chahiye margin ke saath.
Step 1 — Elastic region. Atoms chhote springs ki tarah bonded hote hain. Har bond ko thoda stretch karo toh restoring force displacement mein linear hoti hai. Ek cross-section mein saare bonds ka sum stress aur strain ke beech ek linear relation deta hai:
σ=EεYeh step kyun? Linear atomic-bond restoring force ⇒ linear macroscopic response. E = Young's modulus, slope hai, aur yeh proportional limit tak proportionality ka constant hai.
Step 2 — Yield. Atomic planes par critical shear se aage push karo toh dislocations glide karna shuru kar deti hain — atoms ke planes permanently slip karte hain. Ab kuch strain unloading par wapas nahi aata. Yeh step kyun? Slip irreversible hai, isliye curve straight line se alag ho jaata hai.
Step 3 — Strain hardening. Jaise dislocations pile up aur tangle hoti hain, material ko deform karna mushkil ho jaata hai, isliye stress strain ke saath badhta rehta hai lekin shallow curve ke saath peak σu tak.
Step 4 — Necking & fracture.σu par specimen ek local thin "neck" banaata hai; true area tezi se shrink hoti hai, engineering stress girta hai, aur yeh fracture ho jaata hai.
Elastic slope σ=Eε; elastic deformation ke against stiffness.
Yield stress define karo.
Woh stress jis par permanent (plastic) deformation shuru hoti hai.
Ultimate tensile stress define karo.
Woh maximum engineering stress jo material load drop se pehle sustain karta hai.
0.2% offset kyun use karte hain?
Alloys gradually yield karte hain; offset yield ko 0.2% permanent strain se pin karta hai taaki repeatable ho.
Yield aur fracture ka difference?
Yield = permanent set ki shuruat (part intact); fracture = actual separation.
Margin of safety ka formula?
MoS=σallow/(FoSreqσapp)−1≥0.
Spacecraft mein yield aur ultimate ke liye typical FoS?
~1.25 (yield), ~1.5 (ultimate).
Physically yielding kya cause karta hai?
Dislocations ki irreversible glide (atomic planes ka slipping).
Area double karne se σy change hota hai?
Nahi — yeh ek material property hai; sirf failing force change hoti hai.
Necking ke baad engineering vs true stress?
Engineering girta hai (A0 use karta hai); true badhta hai (shrinking real area use karta hai).
Recall Feynman: 12-saal ke bacche ko explain karo
Ek paperclip imagine karo. Use thoda sa moro aur chhod do — woh seedha wapas spring ho jaata hai (elastic). Use zyada moro aur woh tedha reh jaata hai — tumne "yield" point cross kar liya, yeh permanently badal gaya. Use baar baar aage peeche moro aur yeh toot jaata hai — yeh "ultimate/break" point hai. Spacecraft banane wale engineers exactly measure karte hain ki metal ko kitna kheenchne par woh tedha ho jaata hai (yield) aur kitne par toot ta hai (ultimate), phir woh real forces ko kabhi un ke paas nahi aane dete.
