June 16 2024
(The November 4th version was proofread using ChatGPT)
The fracture mechanism of solid polymer is explained by the fact that the stress concentration caused by constraint of strain leads the stress to locally reach the cohesive strength, causing the polymer structure to fracture. The improvement of the strength i.e. the toughening can be realized by adjusting the bulk elastic modulus which governs the magnitude of constraint of strain
Introduction
1.Basics of material strength
1.1 Deformation and strength of solids
1.2 Deformation and stress concentration of structure materials
1..2.1 Deformation that is dominated by shear deformation
1.2.2 Deformation that is dominated by volume deformation
1.2.3 Mechanism of stress concentration due to constraint of strain
1.3 Relaxation of stress concentration and toughening
2. Deformation and destruction of polymer materials
2.1 Deformation and fracture of polymer materials controlled by shear deformation
2.1.1 Plastic deformation of polymer solids
2.1.1.1 Plastic deformation of crystalline polymers
2.1.1.2 Plastic deformation of glassy amorphous polymers
2.1.2 Softening and necking
2.1.3 Orientation hardening
2.1.4 Failure under the control of shear deformation
2.1.4.1 Fracture of thermoplastic polymer
2.1.4.2 Fracture of thermosetting polymers
2.1.5 Influence of the rate of deformation on the behaviors for the plastic deformation of polymer
2.1.6 Ductile fracture by the creep load
2.2. Deformation and fracture of polymer materials controlled by volume Deformation
2.2.1 Stability of void formation and its expansion
2.2.1.1 Expansion of voids by plastic deformation
2.2.1.2 Expansion of voids by nonlinear elastic deformation
2.2.2 Strain constraint and void expansion stability
2.2.3 Evaluation of fracture behaviors from voids under strain constraint
2.2.3.1 Failure of rubber in pure stretch (Pancake) test
2.2.3.2 Failure of thermoplastic polymer under strain constraint due to notch
2.2.4 Evaluation of the initiation conditions for brittle fracture of amorphous glassy polymers under strain constraint using notch
2.2.5 Unstable deformation of crystalline polymers and their temperature dependence
2.2.6 Influence of deformation rate on the fracture behaviors
2.2.7 Brittle fracture of polymer having a notch by the creep load
2.2.8 Comparison with the fracture of the aluminum alloy
3. Strength design of polymer structure and its evaluation
3.1 Strength design of polymer structures and its toughening
3.2 Strength design of polymer by nonlinear elastic plastic analysis
3.2.1 Strength design of amorphous glassy polymer PC
3.2.1.1 Estimation of PC true stress-strain curve
3.2.1.2 Estimation of fracture condition of PC
3.2.1.3 Predication of toughness of the structure of PC under various boundary conditions
3.2.1.3.1 Effect of the radius of notch tip
3.2.1.3.2 Control of thickness of ligament
3.2.1.3.3 Control of width of specimen
3.2.2 Strength design of crystalline polymer
3.2.2.1 Estimation of true stress-strain curve and volume strain due to voids of POM
3.2.2.2 Estimation of fracture condition of POM 3.2.2.3 Predication of toughness of the structure of POM under various boundary conditions
3.2.2.3.1 Control of the radius of notch tip
5.2.2.3.2Control of the thickness of ligament
3.2.2.3.3 Control of the width
3.3 Toughness evaluation method of polymers and its dependence on boundary conditions
3.4 Evaluation of toughness of polymers by fracture mechanic.
4.Toughening by an adjustment of fine structure
4.1 Effect of number average molecular weight on craze strength and yield stress
4.2 Effect of width of molecular weight distribution on craze strength and viscosity
4.3 Effect of stereo regularity of i-PP on craze strength and yield stress
4.4 Effect of copolymerization on craze strength and yield stress
5. Toughening by release of constraint of strain
5.1 Release of strain constraint and relaxation of stress concentration by reducing bulk Modulus
5.1.1 Reduction mechanism of bulk modulus by void
5.1.2 Relaxation of stress concentration by release of strain constraint
5.1.3 Estimation of the toughness of polymer alloy by nonlinear analysis that uses Gurson model
5.1.4 Estimation of the toughness of polymer alloy by modified Gurson model
5.2 Factors influencing the efficiency of the toughening by elastomer blending
5.2.1 Improvement of toughness by lowering the strength of dispersed phase
5.2.2 Effect of the dispersion state on stability of expansion of void
5.2.3 Improvement of toughness by appropriating the orientation hardening rate
5.2.3.1 Adjustment of the rate of orientation hardening by partial crosslinking 5.2.3.2 Adjustment of the rate of orientation hardening by crystallization conditions
5.2.4 Toughness of polymer blended with elastomer of composite structure
5.2.5 Effect of compatibility between thermoplastic elastomer and resin on toughness
5.2.6 Effect of elastomer orientation of dispersed phase caused by the flow on the toughness
5.2.7 Control of the brittle fracture due to the surface deterioration by the mixture of elastomer
5.3 Other attempt to relax bulk modulus
6. Strength Design of Plastic Composite Material with High Rigidity and Toughness
6.1 Toughening by filling fine particles
6.1.1 Toughening by the blend of inorganic particles
6.1.2 Toughening of rubber by blending carbon particles
6.2 Toughening by the blend of fibers6.2.1 Case of strong adhesive strength on the interface
6.2.2 Case of flaking off in interface by appropriate stress
6.2.2.1 Effect of the strength of flaking off on the toughness
6.2.2.2 Effect of aspect ratio of fiber on the toughness
6.2.2.3 Effect of the contraction force of polymer on the toughness
6.2.3 Example of the improvement of the toughness by the adjustment of the interface strength
6.2.3.1 Toughening of PC blended with glass fiber by the acid modified low molecular weight polyethylene
6.2.3.2 Improvement of both elastic modulus and toughness of PLA by aramid fiber
7. Conclusions