|Politecnico di Torino|
|Academic Year 2009/10|
Master of science-level of the Bologna process in Mechanical Engineering - Vercelli
Objectives of the course
The class consists of a part of general metallurgy (carbon and low-alloy steels; stainless steels; aluminum alloys) and of a part of fracture mechanics and fatigue (notch effects, linear elastic fracture mechanics, fatigue, elastic-plastic fracture mechanics; the two parts are presented contextually and present relevant points of superposition (e.g., brittle-to-ductile transition and environmentally assisted cracking). The purpose of the metallurgy part is the comprehension of the mechanical properties of steels (with particular reference to the different conditions of massive heat treatment and of surface thermochemical treatment, and to the brittle-to-ductile transition) and of aluminum alloys (with particular reference to the casting, plastic deformation, and heat treatment conditions), as well as of the corrosion resistance properties of the stainless steels. The purpose of the fracture mechanics and fatigue part is the comprehension of the mathematical and experimental methods employed to characterize the behavior of metallic materials in presence of defects and of static or cyclic loads (possibly in aggressive environments), and to evaluate the brittle fracture risk of structural components. A purpose common to both parts is the comprehension of the interrelations between mechanical properties and metallurgical characteristics (microstructures, heat treatments).
The student will be able to evaluate the mechanical properties of the most commonly used steels and aluminum alloys, as well as the corrosion resistance properties of the most commonly used stainless steels, on the basis of their respective alloy elements contents, production processes, and service conditions. The student will also be able to estimate the risk of brittle fracture, or fracture consequent to fatigue crack growth, of structural components, on the basis of theoretical principles and experimental results, possibly also in an aggressive environment or in the case of a plastic zone of a not negligible size.
Basic concepts of continuum mechanics and materials science.
CARBON AND LOW ALLOY STEELS
Hints to the production of steels: production by the integral cycle and production from scrap; ladle metallurgy; degassing; ingot casting and continuous casting; forging; hot rolling. Non metallic inclusions in steels: origin, modifications during hot rolling.
Fe-C state diagram (stable and metastable). Recalls: lever rule, Gibbs phase rule. Phase transformations during low cooling of 0.4 wt.% carbon and 0.8 wt.% carbon steels from austenitization temperature; pearlite morphology. Dependence of the phase transformations upon the cooling rate. Martensitic transformation: crystallographic and phenomenological aspects. TTT diagrams: definition, usage, examples (0.8 wt.% carbon steel, 0.4 wt.% carbon steel, alloy steels). Bainite (hints). CCT diagrams: definition, usage, comparison with TTT diagrams.
Normalizing and annealing: execution, purposes (isotropy, stress-relieving, machinability, homogenization), differences.
Quenching and tempering: definitions; transformations during quenching; effects of martensite tempering. Dependence of the quenching results upon the material, the geometry and the quenching medium. Hardenability of steels: definitions of critical diameter, ideal quench, ideal critical diameter DIc; calculation of the DIc on the basis of the composition (standard ASTM A255); Jominy test: execution and meaning. Quenching calculations: concept of equivalent Jominy position; Lamont method; heat conduction equation (one-dimensional case); Biot number and Grossman coefficient; hints to more advanced methods.
Residual stresses, permanent deformations, and brittle fracture risk during steel quenching: origin (diagram of thermo-metallurgical dilation/contraction, deformability of the metallurgical constituents) and influence of geometry, quenching medium, hardenability; use of the less drastic possible medium; step quenching.
Superficial quenching (hardening): definition and purposes; influence of the initial microstructure; conventional thickness. Induction hardening: skin effect; Curie transition; influence of resistivity and thermophysical properties.
Case hardening (carburizing): definition and purposes; carburizing atmosphere (endogas); Bodoir equilibrium; treatment time; quenching and stress relieving; steel grades and production cycles.
Nitriding and ferritic nitrocarburizing: definition and purposes; compound layer and diffusion layer; temperatures; steel grades and production cycles.
Comparison among induction hardening, case hardening, and nitriding (depths, hardness values, treatment durations, thermal stability).
Welding and weldability: description; definition and properties of the HAZ; brittleness of the HAZ; relationship between weldability and hardenability; the Ceq criterion. Welding defects: solidification defects; cracks and residual stresses.
RECALLS OF ELASTICITY THEORY
Plane strain and plane stress states for elastic materials: independence of the stress state from the elastic parameters; stress resolving equations (equilibrium and compatibility) (statement); correspondence between the plain stress and plain strain cases and stiffened elastic constants E' and ν'; yielding (Tresca criterion) in the two cases; stress-strain relationships (statement).
Case of a circular hole in a loaded plate: Kirsch's solution (statement). Case of the elliptical hole in in a loaded plate: Inglis' solution (statement). Limit case for the curvature radius at the ellipse apex approaching zero. Case of a finite width specimen with a central notch: Dixon's solution (statement).
Traction tests of notched specimens: notch strength ratio NSR, strengthening and weakening effects. Plastic deformation and stresses upon the minimum section in the case of a notched specimen. Stress concentration factor in the plastic range Kpf and example of experimental determination (case of a steel hardened and tempered at increasing temperatures).
LINEAR ELASTIC FRACTURE MECHANICS (LEFM)
Theoretical strengths σth and τth of a perfect lattice. σth/τth ratio and fracture mode. Energy balance of the advancement of a crack (Griffith criterion). Extension to the case of ductile materials (Irwin, Orowan). Definition of the strain energy release rate G; definition of the potential energy in the load control and displacement control cases and demonstration of the independence of G from the control mode. Relationship between G and the applied force. Stress concentration at the tip of a defect with a radius of curvature approaching zero (Inglis solution); defect with tip radius equal to the interatomic distance.
The Griffith theory for non-brittle materials: correction for the crack tip plastic deformation.
Stresses and strains at the tip of a crack in plane strain or plane stress, in the I, II and II loading modes (Westergaard solution). Definition of the stress intensity factor KI. Determination of KI in specimens / structures of finite width.
Methods to determine the KI factor by means of finite element calculations: on the basis of the calculated displacements; by using singular elements, particularly with nodes in the position at ¼ side from the crack tip; by calculating G.
Evaluation of the size of the plastic zone at the crack tip. Shape of the plastic zone in the plane, in plane strain and in plane stress. Validity region of the Westergaard solution in a specimen and in a structure. Definition of the fracture toughness KIc and its usage as a fracture criterion. Load triaxiality at the crack tip, tridimensional shape of the plastic zone, effects of the specimen's or component's thickness, formation of shear lips (Anderson). Validity requirements of the LEFM, in the plane and in the thickness. Experimental determination of the fracture toughness KIc: SEN(B) and C(T) specimens, precracking methods, experimental data acquisition and data reduction, validity verifications (ASTM E399 and ISO 12737 standards).
Verification of components with defects: verification against the risk of brittle fracture for propagation of a defect and against the risk of collapse due to overload on the net section; Federsen diagram.
G-R and K-R curves; conditions for the unstable propagation of a crack in the case of materials with a rising R-curve (as a function of the crack growth); load control and displacement control cases. Relationships between the R-curve and the microscopic mechanisms of fracture: cleavage, ductile fracture, influence of the shear lips. Influence of a rising R-curve upon the measurement of KIc; justification of the Pmax/Pq < 1,1 limit.
Brittle and ductile fracture: macroscopic aspects.
The impact tests: qualitative meaning; common characteristics (impulsive load; triaxiality, temperature).
The Charpy test: execution, energy, lateral deformation, ductile fracture area fraction; geometry dependence; usage for materials classification and quality control.
The Pellini test: execution, results (break, no break, no test); significance as a crack arrest test; the nil ductility temperature NDT.
The brittle-ductile transition in the ferritic steels: influence of carbon content, heat treatment, tempering temperature, alloying elements, grain size and quenching cooling rate. Fracture surfaces appearance after the Charpy test as a function of the testing temperature.
Variation of the fracture toughness KIc of quenched and tempered steels as a function of the test temperature; effects of the C and S contents. Correlation between fracture toughness KIc and yielding stress Rp02 of quenched and tempered steels.
Microscopic fracture modes: ductile fracture by microvoid nucleation and growth (influence of dispersed second phases, energy absorption); cleavage fracture (dependence upon the crystallographic planes, river pattern); intergranular fracture (grain boundary embrittlement; ductile intergranular and brittle intergranular cases)
Relationship between microscopic fracture modes and brittle-ductile transition in the ferritic steels; weakest link theory and scatter of the experimental data in the transition range; hints to the probabilistic expression of the brittle-ductile transition curves; hint to the master curve method (statistical expression of the KIc - temperature curve for ferritic steels)
Electrochemical corrosion: anodic and cathodic reactions; electrochemical potential differences; electrolyte resistivity. Uniform and localized corrosion; galvanic corrosion. Sacrificial anode cathodic protection (zinc plating of low alloy steels); protection by passivation (stainless steels, aluminum).
Definition of stainless steel.
Fe-Cr phase diagram (at temperatures higher than 600 °C).
Ferritic stainless steels: examples (AISI 403, 430); heat treatment; grain size control; hints to the σ phase; influence of C upon the mechanical strength and of Cr upon the corrosion resistance; influence of the carbides. Machinability.
Ferritizing and austenitizing elements. Shaeffler diagram: definitions of Creq and of Nieq; ferrite, austenite and martensite regions; biphasic regions; position of the ferritic stainless steels.
Martensitic stainless steels: examples (AISI 410, 420, 440B); mechanical properties and corrosion resistance; relationship between the C and Cr contents. Heat treatment: relationship between austenitizing temperature, carbide solubilization, and post-quenching properties (hardness of martensite or tempered martensite, fraction of residual austenite); quenching and stress-relieving (or tempering).
Sensibilization of stainless steels to intergranular corrosion: sensibilization temperature; carbide precipitation at grain boundaries and local Cr impoverishment; the case of welding.
Pitting corrosion: phenomenology; influence of the Cl- ions; definition and meaning of the pitting index.
Fe-Ni phase diagram (at temperatures higher than 400 °C).
Austenitic stainless steels: properties and uses; position in the Schaeffler diagram; composition (fractions and influences of Ni, C, Cr, Mo); examples
(AISI 304, 304L, 316, 316L); pitting index and marine usage; adverse effect of C; usage of Ti and Nb as carbide stabilizers.
Biphasic (duplex) stainless steels: phases, mechanical properties; usage of interstitial N; usage in stress-corrosion conditions; example: Cr 22 group.
Comparison between Fe and Al alloys: density, elastic modulus, melting temperature. Aluminum alloys: wrought alloy series and cast alloy series (main alloying elements and possible heat treatment of each alloy series). Component production cycles with the two types of alloys.
Principles of the solubilization, quenching, and aging heat treatment in the case of Al-Cu alloys: Al-Cu phase diagram; GP zones and coherent and incoherent precipitates; strengthening as a function of aging temperature and duration; influence of different types of precipitates. Other systems of alloying elements active in the age hardening processes.
Execution of the heat treatments: solubilization, annealing, and aging temperatures; quenching severity and media; quenching shortcomings (residual stresses, dimensional instability); effectiveness in the case of large sections (C curves); similitude and differences in respect to the quenching of steels. Standardized metallurgical states F, O, H, T3, T4, T5, T6.
Cast aluminum alloys: Al-Si phase diagram; effects of Si on castability. Presence of undissolved Si (as a second phase) in the castings; second-phase strengthening and strengthening due to microstructural refinement (eutectic alloys); indicative trend of yield stress and fracture elongation as a function of the Si content. Usage of Na and Sr to modify the Si morphology (from lamellar to nodular). Usage of grain refiners (hint); effect of the interdendritic distance (SDAS) upon the mechanical properties.
Fatigue of metallic materials: phenomenological description; fatigue tests of smooth specimens: definition of the σmin, σmax and R cyclic parameters; example of nucleation mechanism (plastic); aspect of the fracture surfaces (nucleation, propagation, and final fracture zones); S-N (Wholer) and S-N-P diagrams.
Conditions needed to describe the stress state at the crack tip by the KI factor; cyclic plastic zone; plastic wake. Dependence of the fatigue crack growth rate upon the cyclic variation of the stress intensity factor ΔK and upon the load ratio R. Paris diagrams: properties of the regions I, II and III, ΔK threshold (ΔKth); critic K (Kc). Empiric fatigue crack growth laws: Paris law, others. Relationship between Kc and KIc.
Qualitative Paris curves at varying R. Crack closure due to compressive residual stresses in the plastic zone and in the plastic wake, hints to other closure mechanisms (roughness; corrosion products; fluids; phase transformations). Definitions of: opening load Pop, opening stress intensity factor Kop, effective cyclic amplitude of the stress intensity factor ΔKeff. Paris diagrams expressed by employing ΔKeff instead of ΔK; justifications of the differences due to the load ratio in the ordinary Paris diagrams.
Effect of isolated overloads on the fatigue crack growth: impossibility of describing the stress state at the crack tip on the basis of the current cyclic c only in the case of cyclic loads of variable amplitude; effects of initial acceleration and successive retardation consequent to a single overload; influence of the compressive residual stresses ahead the tip (stress reduction) and behind the tip (closure); qualitative evaluation of the retardation (comparison among the current cyclic plastic zone and the plastic zones of previous overloads).
Qualitative examples of N-a diagrams: constant load amplitude and constant displacement amplitude cases; cases with different initial crack length and different constant load amplitudes.
Growth of short cracks: definition of either microstructurally short or mechanically short cracks; inapplicability of the K factor to the short cracks; higher apparent crack growth rate of short crack, as evaluated against apparent ΔK.
Microscopic crack growth mechanism and aspect of fatigue crack growth fracture surfaces.
Fatigue crack growth measurement according to the ASTM E647 standard: maximum allowed plastic zone size in respect to the specimen's width; possible dependence on the specimen's thickness; crack length measurement methods; test execution (precracking, ΔK-decreasing fatigue and determination of ΔKth; constant load amplitude ΔK-increasing fatigue); calculation of the Paris diagram (secant method and hints to the polynomial method); scatter of the measurement points; determination of th opening load with the compliance method (principles).
Inspection of structures subjected to fatigue: maximum crack length not revealable by non-destructive tests; maximum allowable crack length; optimal inspection intervals.
ENVIRONMENTALLY ASSISTED FATIGUE
Environmentally Assisted Fatigue, EAC: concept; diagrams of crack growth speed as a function of stress intensity factor KI with static load, regions I, II and III, threshold value KIEAC; cases of either quasi constant or linearly increasing region II behavior. Types of EAC: Stress Corrosion Cracking SSC, hydrogen embrittlement, corrosion-fatigue.
SSC: qualitative description; anodic behavior of the crack tip and passivation of the crack faces; causes of the lack of passivation of the tip (fracture of the passive layer due to the plastic deformation of the underlying metal; lesser nobility of the tip; corrosion conditions close to the limit between passivation and non-passivation).
Hydrogen embrittlement: cases of embrittlement either due to H coming from the corrosive environment, or due to H already present in the metal following previous treatments; H solubility and diffusivity in metallic lattices at room temperature; variation of H solubility as a function of the stress state; effects of H on the interatomic bonds; crack growth by progressive embrittlement at the tip.
Possible concurrence of SSC and hydrogen embrittlement.
Examples: K ' log(da/dt) diagrams of an aluminum alloy subjected to SSC in different aging conditions and of a quenched and tempered steel subjected to hydrogen embrittlement with different H2 partial pressures.
Integration of EAC crack growth laws; inapplicability of the K ' log(da/dt) diagrams to short cracks (due to inapplicability of the K factor and due diversity of electrochemical conditions).
Apparent variation of KIEAC as a function of loading rate.
Relationship between the the EAC crack growth (KIEAC threshold and da/dt speed for given K) and the yield stress of quenched and tempered steels; possible justifications.
Corrosion-fatigue: competition and concurrence between the EAC and fatigue mechanisms; effect of the frequency; da/dN - ΔK curves in corrosion-fatigue conditions.
EAC measurements: constant load and constant displacement methods, respective trends of crack length and K factor in time.
ELASTIC-PLASTIC FRACTURE MECHANICS
Goals of the elastic-plastic fracture mechanics: evaluation of the fracture toughness of materials with high KIc/σy ratio; verification of components with defects in conditions intermediate among those of brittle propagation fracture and of plastic collapse.
The CTOD: qualitative definition and empirical observations. Effective crack length aeff and effective stress intensity factor Keff (Irwin model); elastic displacement at the tip of a crack opened at mode I (Westergaard solution); demonstration of the correlation between CTOD and KI in the small plastic zone case, by means of the evaluation of the CTOD displacement at the physical crack tip on the basis of the displacement field associated with Irwin's Keff and aeff. Geometrical CTOD definitions. Direct and indirect CTOD measurements; hints to the plastic hinge hypothesis for the CTOD determination on the basis of COD measurements in the case of three point bending specimens.
Premises to the introduction of the J parameter: elastic-plastic behavior and non-linear elastic behavior; limits of the approximation of an elastic-plastic behavior with a non-linear-elastic model (load monotony, small plastic deformations); comparison with the approximation of the true σ-ε curve with the engineering one. Application to the crack tip stress state: regions at increasing distance from the tip, in which either a linear elastic approximation is sufficient, or a non-linear elastic one is sufficient, or none of the two (large deformations region).
Definition of J as the strain energy release rate in the non-linear elastic case: recalls on the definition of G; equality of G and J within the linear elastic limit; demonstration of the independence of J on the control type (load or displacement). Relationship between J and the load within the linear elastic limit.
Inapplicability of the strain energy release rate definition of J in the case of elastic-plastic materials, and alternative definition of J as the incremental ratio of the energy adsorbed while loading a specimen in respect to the specimen's initial crack length.
Definition of J as a line integral (Rice); nullity of the integral on a closed line in absence of singularities (enunciate); defition of J applied at a crack tip and demonstration of its independence from the integration path. Equality among the different definitions of J.
Usage of J as a parameter characterizing the crack tip stress state (HRR theory): need and definition of a non-linear elastic stress-strain law; crack tip stress field (enunciate); dependence upon r(-1/(n+1)). Approximate application in the case of elastic-plastic material and validity limits.
Recall of the quantitative relationships among J, G, KI and CTOD in the linear elastic case; extension of the relationship between J and CTOD to the non-linear elastic or elastic-plastic case. Regions at increasing distance from a crack tip, in which the stress state can be described either with the KI parameter (K-dominated zone) or with the J parameter (J-dominated zone or HRR zone), or by none of the two (large plastic deformation region at the tip); qualitative representation on the double logarithmic σ-r diagram and in cases with increasing plastic zone sizes (in respect to the ligament size).
J- Δa curve: region of crack tip blunting and region of stable crack propagation by plastic tearing. Microscopic stable crack growth mechanisms (by microvoid growth and coalescence at the tip); influence of the triaxial stress state. Demonstration of the linear relationship between J and Δa in the blunting region (by means of the correlation among J, CTOD and Δa). Transition from blunting to plastic tearing and definition of JIc. Definition and conventional determination of Jq in the J ' Δa plane (standard ASTM E1820). Analogies with the conventional definition of the Rp02 yield point in traction. Definition and conventional determination of δq according to the same E1820 standard: δ - Δa curves and analogies with the JIc conventional definition and determination. Limits in which Jq e δq can be qualified as JIc e δc: correspondence between the limitation for JIc and for δc; comparison with the KIc validity limit; possibility of performing JIc or δc, but not KIc, measures in the case of materials with high thoughness.
Point by point determination of J - Δa curves. Multi-specimen and single specimen methods. Measurement of Δa after cracking (heat tinting, fatigue marking) or during the test (potential drop method; compliance method and its shortcomings). Calculation of J: discussion of possible alternative methods; partition of elastic and plastic components; plastic area method. Justification of the plastic area method on the basis of the strain energy release rate definition of J. Need of corrections to the plastic area method due to the crack growth. Plastic area method according to the ASTM E1820 standard in the multi-specimen and single-specimen cases.
Experimental determination of the δ ' Δa curves according to the ASTM E1820 standard.
Verification of components with elastic-plastic fracture mechanics methods. Empirical curve for verification by comparing the total service deformation and the material's CTOD (CTOD design curve). Determination of the service applied J and its comparison with the JIc: possibility of finite element calculation; usage of tabulated solutions. Typical form of the tabulated J calculation solutions; their dependence upon the plastic flow properties and particularly upon the hardening exponent. Justifications of the differences among formulas employed to calculate J during laboratory measurements and during component design. Failure assessment diagrams obtained from J calculations.
Laboratories and/or exercises
Classroom examples and exercises on the LEFM: KI calculations for through defects, for inner circular or elliptic defects and for superficial semi-elliptic defects; safety factor calculation; defect classification after non-destructive tests (pressure vessel standards).
Classroom examples and exercises on the fatigue crack growth: integration of the Paris Law in the constant load, constant geometrical factor case; fatigue service life calculations.
Computer lab exercise: finite element calculation of a crack tip stress field and of the KI factor in a bidimensional case, by using singular elements (quadratic elements with nodes moved to ¼ side). Comparison of the calculated KI with the analytical solution. Comparison of calculated σx and σy in the ligament with the Westergaard solution and comments on the size of the K-dominated zone. Shape of constant equivalent Von Mises stress curves, in the plane stress and plane strain cases.
Visit to laboratories of the DISMIC department, in the central site. Performance of Charpy tests on low alloy steel specimens, with V-notch, at room temperature and after liquid nitrogen cooling. Working principles of scanning electron microscopes; signals obtained from secondary electrons, backscattered electrons, and X-rays (EDS/WDS sensors). SEM observation of fracture surfaces obtained after different types of mechanical tests; recognition of morphologic characteristics of different fracture mechanisms. Visit of a fracture mechanics laboratory: illustration of a test machine, of various types of CT and SENB specimens, and of the current fracture mechanics test. Light microscope observation of steel metallographic specimens with different C contents and in different heat treatment conditions.
A single textbook containing all the topics presented in the class is not available. The Nicodemi textbooks (particularly the 2nd volume, Acciai e leghe non ferrose) or the Burdese textbook are recommended for the metallurgical topics. The Anderson textbook (in English) is preferred for the fracture mechanics topics, whereas the textbooks of Vergani and Rossetto are signalled as alternatives.
W. Nicodemi, Metallurgia: principi generali. Bologna: Zanichelli, 2000.
W. Nicodemi, Acciai e leghe non ferrose. Bologna: Zanichelli, 2000.
A. Burdese, Metallurgia e tecnologia dei materiali metallici. Torino: UTET, 1992.
T. L. Anderson, Fracture mechanics: fundamentals and applications. Boca Raton, FL, USA: Taylor & Francis, 2005
L. Vergani, Meccanica dei materiali. Milano: McGraw-Hill, 2006
M. Rossetto, Introduzione alla fatica dei materiali e dei componenti meccanici. Torino: Levrotto & Bella, 2000.
Revisions / Exam
The exam is oral.
Programma definitivo per l'A.A.2009/10