MATERIAL BEHAVIOR A. Types of Behavior Models

To meet design requirements, materials must have adequate mechanical strength and be able to resist different types of corrosion, wear, etc., so that the various types of failure modes can be avoided. Table 1 is a listing of the main properties and attributes used for material characterization.

Material behavior can be analyzed by developing models related to material attri-butes, required functions and manufacturing processes. Due to the large number of factors involved, the problem is often simplified by considering blocks of knowledge, correspond-ing to specific mechanisms and functions. Each block of knowledge represents a simplified model that relates some properties to the required functions. Using the state-of-the-art material engineering criteria which may be based on practical experience, it is possible to optimize performance. The results of this analysis are summarized in the definition of design.

In the next step, two groups of behavior models shown in Fig. 4 will be discussed.

The first group is the behavior models used to avoid basic failure modes. These models relate material attributes—generally known as ‘‘properties’’—which are well defined and individually determined. These properties are density, elastic modulus, tensile strength, elastic limit, elongation, fracture toughness, shape and size, etc. These test and criteria properties have specific operational definitions. Although these basic failure modes are usually present in all the metal designs, only the criteria used to avoid or minimize damage occurrence will be illustrated here.

The second group of behavior models includes attributes that involve the complex interrelation of a number of variables associated with the material, its manufacturing processes, and service conditions.Weldability, wear resistance, localized corrosion resis-tance, embrittlement, biocompatibility, etc., are among these attributes. Material weld-ability, for instance, is a broad and relative concept that refers both to the ease with which a material can be joined through some welding processes, and the resulting weld fitness in service.

For the second group of blocks of knowledge, physical metallurgy is used together with the laws of mechanics. Crystalline structure, microstructural and compositional char-acteristics, grain size and shape, dislocation density, second-phase particles, segregations, non-metallic inclusion shape control are among the concepts applied. In this case, aniso-tropy and the typical heterogeneities inherent to many materials become evident. These material attributes and criteria have no accurate operational definitions.

B. Behavior Models to Avoid Basic Failure Modes Based upon Well-Defined Material Properties

Behavior models which are used to avoid basic failure modes usually treat materials as being homogeneous, continuous and isotropic, and apply the laws of continuous mechanics. The properties used are those involved in the basic formulas of mechanical design and those typically used to characterize material properties provided in engineering handbooks, specifications, and supplier catalogs. Designers are typically interested in strength, creep strength, ductility, creep ductility, notch toughness, modulus of elasticity, thermal expansion, and fatigue strength. These models state that the combination of some properties may impose performance limitations, in addition to those limitations imposed by individual properties. Using these models, it is possible to develop designs that avoid basic failure modes, such as uniform corrosion, yield, ductile fracture, creep, elastic instability, brittle fracture, and fatigue. The criteria developed in detail by Ashby [11]

can be applied in this step in the review process of design.

The primary behavior models intended to avoid some of the basic failure modes will be discussed subsequently.

Table 1 Material Characterization

Material properties Modulus of elasticity (Young, shear), Poisson’s ratio, ultimate tensile strength, yield strength in tension, shear strength, compressive strength, ductility, elongation, impact strength, fracture toughness, modulus of resilience, fatigue endurance limit, hardness, damping, creep strength, creep-rupture strength, thermal conductivity, thermal diffusivity, thermal expansion, specific heat, melting point, density, corrosion rate, electric conductivity

Material parameters Chemical composition, chemical homogeneity, phases, crystallography, grain size, second-phase particle, non-metallic inclusions, dislocations, vacancies, texture, porosity

General attributes Shape, size, cost, durability, availability, fabricability, weldability, castability, machinability, formability, hardenability, hot working parameters, heat treatment parameters, producibility, maintainability, surface finish, esthetic appeal, maintainability, biocompatibility, conformance to standards, energy requirements

Figure 4 Block of knowledge used in failure design.

1. How to Avoid Uniform Corrosion

The first block of knowledge corresponds to material behavior during exposure to the ser-vice environment. In this section, general metal loss due to corrosion=oxidation and=or erosion will be discussed. If the metal loss rate among different points in an area varies by a factor of 4 or less, the damage is considered uniform.

The material selected should have a corrosion rate in the corrosive environment and at the design temperature which provides allowable material loss during the design life of the component. In some cases, design life is determined prior to the design process which may depend on both technical and economic factors. In the petrochemical industry, for example, a design is developed for a 10–15-year life extent, whereas in nuclear projects it is developed for a 40-year life extent.

Corrosion allowance is determined in accordance with the criteria set forth in the design code and the special conditions of the process. Corrosion allowance may be 1.6 or 3 mm; it is usually lower than 6 mm for economic reasons. When selecting the generic material, both corrosion resistance and the cost factor should be optimized. By using this behavior model, the risk of failure modes due to uniform corrosion is minimized. For uniform corrosion upon exposure to strongly corrosive environment, such as strong acids, strong alkali, salt water, and aerated water, the model that is the fraction of wall loss dur-ing thinndur-ing, due to uniform corrosion, is equivalent to ar=t where time is (a), corrosion rate is (r), and thickness is (t). This model provides a preliminary definition of the generic type of material suitable for design.

2. How to Avoid Ductile Failure Mode

The following block of knowledge refers to both the capacities, the load transfer capacity of the material, and the method to avoid ductile failure. This failure mode is related to

‘‘static’’ stresses and ‘‘static’’ mechanical properties, and is applicable to structures sub-jected to stresses of approximately constant magnitude, or where the total number of cycles imposed in the course of the working life is comparatively small.

Plastic deformation, which may lead to the component collapse or rupture, should be avoided. Both yield properties which result when the elastic limit of the material is exceeded and potential creep deformation are considered in this model. When a material is exposed to temperatures above 1=3 Tm(melting point) and is mechanically loaded, time-dependent creep occurs. When structures are exposed to the creep temperature range, the material should be measured to avoid unacceptable deformations or rupture throughout its useful design life.

For the selected material, the required shape (casting, forging, plate, pipe) and the possible manufacturing processes should be considered first. Then, in accordance with the design code (e.g., ASME, ANSI) adopted, the specification for the material to be applied is selected and allowable design stresses at the operation temperature are deter-mined [12].

The minimum wall thickness for the size of equipment and its pressure is subse-quently calculated with respect to the allowable design stress from the code. The stresses taken into account are the ones known as ‘‘primary stresses’’, which equilibrate the applied loads, and ‘‘secondary stresses’’, which are self-equilibrating. Stresses are caused by any combination of continuous or cyclic loads, of an either mechanical or thermal origin [13]. By assuming that the material is isotropic and applying different criteria (Von Mises’s equivalent stress, Tresca’s criteria) along with the allowable design stress, the dimension of the product can be calculated. The allowable design stress of the previously selected

material exposed to the design temperature is determined by means of the design code.

Uniform corrosion allowance—previously determined—should be added to the calculated material thickness.

The criterion applied to avoid plastic deformation states that the calculated stress intensity or effective stress must be lower than the yield and design life creep-rupture stres-ses of the material:

se syðVon MisesÞ; where se¼ ð1= ffiffiffi p2

Þ½ðs₁ s₂Þ²þ ðs₂ s₃Þ²þ ðs₃ s₁Þ²¹⁼²; where s1> s2> s3are the principal stresses.

When effective stress is exceeded somewhere within the component it does not neces-sarily indicate plastic collapse of the entire structure. Primary stresses may locally exceed yield, within certain limits, provided there is enough ductility to allow the material to yield without cracking. Plastic collapse occurs when primary stresses are uniform on the entire structure and exceed effective stress. To prevent an incremental collapse or thermal stress ratchet in each loading cycle, the total elastic stress intensity range, considering residual and applied stresses, should be limited to twice the yield stress.

According to Hooke’s law, the elastic deformation is usually calculated as e₁¼ ½s1 nðs2þ s3Þ=E;

where e1is the principal deformation in direction 1, s1, s2and s3are the principal stresses, E represents the elastic constants of the material (Young’s modulus), andn is Poisson’s ratio. In addition to the material properties, the resistant section area is also an element of this calculus.

Design codes deal with uncertainties that arise from data, such as properties and cal-culation methods, by using safety factors to provide a safety margin. Allowable design stresses, used in calculations, are generally 2=3 times lower than yield stress or design life creep-rupture stress. Other restrictive criteria, such as limiting the allowable design stress to 1=4 times the ultimate stress, are applied as well. The safety factor generally ranges from 1.5 to 4.0. When welds are made, allowable design stresses are reduced due to a factor known as ‘‘joint efficiencies’’, depending on the specified non-destructive tests (NDT) level.

The application of this module guarantees an adequate mechanical strength capable of minimizing plastic deformation risk as well as considering thickness loss due to uniform corrosion throughout the design life.

3. How to Control Stiffness

In addition to strength, stiffness must also be calculated. Structure stiffness is based on the maximum elastic deflection under a load. Stiffness depends on both the geometry (proper-ties throughout the section) and elastic modulus of the material. If the product to be designed is an element that must withstand not only tension loads but also bending, torsional, and axial-compressive loads, the combined effect of the applied loads (type, shape, and size) and the material properties associated with stiffness must also be deter-mined. The moment of inertia of the section is used in the calculation. By applying this block of knowledge, failure due to structural distortion is avoided.

4. How to Avoid Elastic Instabilities

Design for those elements subjected to axial compression should be included to avoid not only plastic collapse but also elastic instabilities. Elastic instabilities may cause Euler

buckling and local buckling. The occurrence of this failure mode depends on the geometry of the elements and on Young’s modulus of the material. When the element subjected to compression is very long or slender, it has a greater tendency to buckling. Slenderness ratio equals l=r, where l is the length of the member and r is the least radius of gyration of the section. The radius of gyration is calculated as

r¼ ðImin=AÞ¹⁼²;

where I_minis the moment of inertia and A is the cross-section area. In general, the relationship between Young’s modulus (E) and density (r), E=r should be maximized to increase stiffness;

by doing so, yield occurs before buckling, whereas by increasing sf=r, strength also increases;

hence buckling occurs before yield. For example, the critical load needed for a column under compression to become instable is proportional to EI=l², where E represents Young’s modulus, I the moment of inertia of the section and l the column length.

5. How to Minimize Stress Concentrations

The elastic stresses calculated above are nominal values, which do not take into account local discontinuities, such as holes, notches or section changes. Even on a structure where stress intensity has been limited by yield criteria, there may exist highly localized regions where peak stresses are several times higher than yield. Maximum local stresses on a struc-ture can be determined by considering nominal stresses multiplied by a stress concentra-tion factor, and can be estimated through a detailed stress analysis or by using approximate formulas that account for the most common cases. The design should be verified to confirm whether there are stress concentration points that might activate failure mechanisms due to brittle fracture, corrosion or fatigue.

6. How to Avoid Brittle Fracture

Brittle fracture is associated with very little or no plastic deformation and with a cleavage fracture or intergranular surface, unlike ductile fracture, which is associated with a fibrous surface. A material may fail in an unstable and catastrophic brittle manner under stresses even lower than the allowable design stresses used to avoid ductile failures. This may occur in a given combination of material properties and applied stress levels.

The material property that controls brittle fracture strength is toughness. Other factors that have an effect on brittle fracture are material thickness, local stress level, including nominal stresses, residual stresses and stress concentration factors, temperature, and loading rate. Carbon and low-alloy steels undergo a transition from ductile failure mode to brittle failure mode at low temperatures. Resistance to crack propagation is mea-sured through fractomechanical tests; crack propagation will occur when the stress inten-sity at crack tip, K, reaches a critical value Kc(MPa m¹⁼²). Kcvalues are experimentally obtained through fatigue precracked test pieces. The critical stress intensity for fracture under plane strain (Klc) corresponds to mode I loading (Tension) under plane-strain con-dition. The critical energy-release rate at fracture is

G_Ic¼ Kc2ð1  n²Þ=EðkJ=m²Þ

where E is Young’s modulus and n is Poisson’s ratio. Brittle materials are those that remain elastic until breaking (break occurs before yield).

In the case of brittle metals, the plastic zone associated with the tip of the crack is approximately 0.1–1 mm in diameter; whereas in ductile metals, the diameter of the plastic zone at the tip of the crack can reach 100 mm. For brittle materials, fracture toughness KIc

has relatively low and properly defined values; but when materials are very tough, with significant plastic deformation before break, KIc is estimated by measuring the critical J-integral (Jc):

K_Ic¼ ðEJcÞ¹⁼²

When design is intended to minimize brittle fracture risk, as in the case of pressure vessels where safety must be maximized, Fracture Mechanics is applied to the design so that yield occurs before break or leak occurs before break, while attempting to keep thick-ness low for costs and mass reasons. Yield before break is accomplished by maximizing the KIc=syratio (fracture toughness=yield stress); whereas leak before break is accomplished by maximizing KIc2=sy. In both cases, a high yield stress is required to minimize material thickness. The latter ratio can be interpreted as being proportional to the size of the zone close to the tip of a crack (the plastic zone in ductile solids). The global approach of fracture assumes that failure can be described in terms of a single parameter, such as KIcor JIc.This approach may yet prove to be questionable in complex situations.

This is the reason why local approaches of fracture have also yet to be developed [14].

The material to be selected should have adequate toughness to withstand the lowest design temperature. If the material is welded, both the HAZ and the weld metal shall have adequate toughness in their final condition. The design must be reviewed to minimize the presence of notches and defects that concentrate stresses. For some materials, toughness can deteriorate during service at high temperatures due to metallurgical changes. These aspects will be discussed subsequently.

Both material toughness and uniform corrosion resistance are elements in the selection of the material, through an iterative process, which includes mechanical calculations and costs.

7. How to Avoid Impact Damage Through Design

A material may have good tensile strength and adequate ductility under static loads; how-ever, it may fail when loads are applied at a high velocity. Impact strength, provided the material is stretched below the elastic limit, is associated with the resilience modulus, R:

R¼ sy2=2EðJ=m³Þ

where E (GPa) is Young’s modulus, and represents the slope of the linear elastic part of the stress–strain curve, sy (GPa) being the stress to which the stress–strain curve is 0.02% deflected from the elastic line.

Resilience is the measure of the capacity the material has to absorb energy in the elastic field. The resilience modulus represents the maximum energy the material is able to store in an elastic manner, without causing damage, and it can be released when it is discharged=unloaded: in some cases, the element must be designed so that it is sufficiently resilient to absorb the kinetic energy associated with the impact as elastic energy. In other cases, design can be developed in a static manner by increasing loads by a factor of 2 or 4 so that impact loads are accommodated [15].

If the design contains elements that must be capable of storing elastic energy per volume unit, without deformation or breakage due to metal fatigue, as in the case of a spring, the s²=E ratio should be maximized regardless of its shape.

When the elastic limit is exceeded, the problem of toughness should be considered.

8. How to Avoid Fatigue Failure

Fatigue failure refers to the deterioration of a component caused by crack initiation and=or crack growth. When mechanical loads alternate, there may be a risk of fatigue failures. In fatigue failures, a crack grows in each loading cycle until the remaining component fails due to ductile or brittle fracture. This phenomenon can occur at stress levels lower than the allowable stresses for static loads. The most important character-istic of a fatigue failure is that some components made from ductile material fracture without revealing any indication of prior plastic deformation, and failure occurs at stress values below the elastic limit of the material. In the past, due to the fracture surface appearance analogous to brittle cleavage fracture, it was incorrectly supposed that a material changed its structure due to the application of cyclic forces and become crystal-line and brittle.

To avoid fatigue failure in component design, a stress analysis considering pressure and temperature variations, mechanical vibrations, winds, and fluid pulsation during design life is performed. The results of this analysis, together with stress concentration fac-tors, permit the establishment of the local stress range and the number of cycles. By using the S=N curves set forth in the design code adopted, for example, ASME Code VIII Div 2 [16] or BS 5500 [17], it is possible to calculate fatigue life.

Fatigue life refers to the number of stress cycles of a particular magnitude required to cause the fatigue failure of the component; whereas fatigue limit refers to the magnitude of stress range under constant amplitude loading corresponding to infinite fatigue life or a number of cycles large enough to be considered infinite by design codes.

Cumulative fatigue damage is defined as theP

n=N  1.0 ratio where n is the number

n=N  1.0 ratio where n is the number