Casting, Metal Forming, Joining and NDT

Nondestructive testing methods

Nondestructive testing (NDT) examines a component without damaging it, so the part remains usable after inspection. Each method responds to a different physical phenomenon, and the choice depends on where the defect lies and on the material's electrical and acoustic properties.

Liquid penetrant testing works by capillary action: a low-viscosity dye is drawn into cracks that open to the surface, and a developer then makes the trapped dye visible. Because it detects only surface-breaking discontinuities, it cannot identify volume defects such as internal porosity, shrinkage cavities or inclusions in a casting.

Radiography, using X-rays or gamma rays, records differences in radiation attenuation. A void or inclusion absorbs the beam differently from sound metal, so it appears as a darker or lighter region on film or a detector. X-ray computed tomography reconstructs such attenuation data into a three-dimensional volume. Planar cracks lying parallel to the beam may be missed, because they change the absorption very little.

Ultrasonic testing sends high-frequency elastic waves into the part and locates discontinuities from the echoes reflected at their boundaries. It is the standard volumetric method for internal flaws in forgings and railway wheels. However, materials with high damping, such as grey cast iron, attenuate and scatter the waves strongly, so sub-surface inspection becomes unreliable.

Acoustic emission detects the transient elastic waves released by a growing crack, so it suits in-service monitoring rather than a one-time scan.

Eddy current testing induces currents in an electrically conductive part by electromagnetic induction. A flaw alters the induced currents and hence the coil impedance. The method requires a conductor, so an electrical insulator such as alumina cannot be tested this way.

• capillary action — the spontaneous entry of a liquid into a narrow opening without applied pressure. e.g., A tight surface crack fills with penetrant during the dwell time.
• attenuation — loss of beam intensity as it passes through a material. e.g., A denser or thicker section gives greater attenuation in radiography.
• volumetric method — a technique that detects flaws throughout the thickness, such as radiography and ultrasonics, in contrast to surface methods.

Casting and forming defects

Casting and forming defects are named for their cause, and recognising the cause tells you which process step to correct. In casting, misrun is incomplete filling that occurs when the metal solidifies prematurely before the cavity is full. Crush is the displacement of the mould cavity by an oversized core, which gives excess metal in one region and a deficient section in another. An expansion scab forms when liquid metal penetrates behind the surface layer of a sand mould. Pin holes are fine gas porosity caused by gas evolved during solidification. Hot tearing is cracking that occurs when contraction is restrained in certain areas while the casting solidifies and cools.

In forming, a cold shut is a surface discontinuity produced in forging when two metal flows meet without fusing. Earing is the wavy rim formed on a deep-drawn cup because the sheet has planar anisotropy. Edge cracking appears at the edges of rolled strip, which cool faster and are less ductile. Alligatoring is the splitting of the ends of an ingot or slab in rolling, caused by non-uniform deformation at the ends. Chevron or fir-tree cracking is an internal fracture along the axis in extrusion when the reduction is large and the flow is non-uniform. Stretcher strains are Lüders bands that appear on sheet during forming, and centre burst is an internal axial fracture in drawing. Flashline cracking is a crack that forms at the flash line of a forging.

• misrun — incomplete filling caused by premature freezing. e.g., A thin section poured with metal that is too cool remains unfilled.
• expansion scab — a rough surface defect from metal penetration into the mould surface. e.g., Liquid metal forces its way under the facing sand of a mould.

Welding heat input and weld area

In arc welding, the power delivered by the arc is P = VI, but only a fraction \eta_h, the heat transfer efficiency, reaches the workpiece, so the effective power is \eta_h P. Of this, only a fraction called the melting factor f_m is used to melt the base metal, and the remainder is conducted away into the plate. The volume of metal melted per second is f_m \eta_h P / u, where u is the unit melting energy in J/mm^3. Dividing by the travel speed v gives the weld cross-sectional area A = f_m \eta_h P/(u\,v). This relation is used whenever the weld area must be computed from the power and speed.

The heat input per unit length of weld is H = \eta V I / v. Two welds made with the same efficiency and voltage have equal heat input when the ratio I/v is the same, which gives the direct proportionality used to compare currents and speeds.

The heat input per unit volume of weld metal is H_v = \eta V I/(v A), where A is the weld cross-sectional area. Rearranging gives v = \eta V I/(A H_v), which is used when the weld area and the required heat input per unit volume are given.

Example: with P = 2000 W, \eta_h = 0.7, f_m = 0.4, u = 5 J/mm^3 and v = 4 mm/s, the weld area is A = (0.4)(0.7)(2000)/(5 \times 4) = 28 mm^2.

Neutral point in rolling

As a strip passes through the roll gap, its speed changes from the entry speed to the exit speed. Near the entry the roll surface moves faster than the strip, which is called backward slip, and near the exit the strip moves faster than the roll surface, which is called forward slip. Between these regions lies the neutral point, also called the no-slip point, where the roll surface velocity equals the sheet velocity and the relative slip is zero. Friction acts toward the neutral point from both sides, so its direction reverses there.

Front tension increases the exit velocity of the strip and therefore enlarges the forward slip region, which shifts the neutral point toward the roll entrance. Part of the deformation is assisted by the tension, so the roll pressure and the rolling load decrease. Back tension has the opposite effect on the position of the neutral point.

• no-slip point — the neutral point, where the roll and sheet velocities are equal.
• forward slip — the condition in which the strip leaves the roll faster than the roll surface moves.

Welding process applications

Each welding process has a characteristic field of use set by its heat source, its shielding and whether the electrode is consumed. Submerged arc welding runs under a granular flux blanket, deposits metal at high rates, and is limited to the flat position. Electroslag welding is a continuous vertical process suited to thick sections. Shielded metal arc welding is versatile and portable and is widely used for surfacing and repair. Resistance spot welding fuses overlapping thin sheets by resistance heating under pressure.

In tungsten inert gas welding the tungsten electrode is non-consumable, and any filler metal is supplied separately. Friction welding joins parts in the solid state, and soldering and brazing use a filler metal that melts below the melting point of the base metals. Thermit welding uses the aluminothermic reaction 2Al + Fe_2O_3 \rightarrow Al_2O_3 + 2Fe to produce molten iron for joining.

The width of the heat-affected zone depends on the power density of the heat source. Electron beam welding concentrates very high power density into a narrow, deep weld, so its heat-affected zone is the smallest among the common processes. Submerged arc and oxy-acetylene welding deliver heat over a broad area and produce wider heat-affected zones.

Maximum possible reduction in rolling

Steady rolling requires that friction can draw the strip into the roll gap, so the friction angle must be at least the bite (nip) angle \alpha. This gives \mu \ge \tan\alpha, that is \alpha_{max} = \arctan\mu. The geometric draft is \Delta h = 2R(1-\cos\alpha), where R is the roll radius, so the maximum possible draft is \Delta h_{max} = 2R\left(1 - 1/\sqrt{1+\mu^2}\right). For small \mu this reduces to \Delta h_{max} \approx \mu^2 R. The result is independent of the initial thickness, so for the same roll radius the ratio of maximum reductions under two friction conditions is the square of the ratio of their coefficients. For example, the cold-to-hot ratio is (0.04/0.4)^2 = 0.01.

For a single pass with a specified reduction, the bite condition gives the minimum friction. From \cos\alpha = 1 - \Delta h/(2R) it follows that \mu_{min} = \tan\alpha = \sqrt{1-\cos^2\alpha}/\cos\alpha. Example: for R = 300 mm and \Delta h = 6 mm, \cos\alpha = 0.99 and \mu_{min} \approx 0.14.

Extrusion force estimation

Extrusion force is estimated with an extrusion constant k, a flow-stress-like value in MPa that lumps the effects of flow stress, strain hardening, friction and inhomogeneous deformation. For ideal extrusion, the force is F = A_0\,k\,\ln(A_0/A_f), where A_0 is the initial billet area and A_f is the final product area. The logarithmic term is the true strain of the extrusion.

The ideal plastic work per unit volume is W = \int \sigma\,d\varepsilon. For a perfectly plastic material whose flow stress depends only on strain rate, the stress does not change with strain at a constant strain rate, so W = \sigma\varepsilon with \varepsilon = \ln(A_0/A_1). Because area varies as the square of diameter, \varepsilon = 2\ln(D_0/D_1). Example: an area reduction ratio of 4 gives \varepsilon = \ln 4 = 1.386, and with \sigma = 50 MPa the work is W = 69.3 MJ/m^3.

Gating system design

A gating system carries molten metal from the pouring basin through the sprue and runner into the gate and cavity. The cross-sectional areas, written as a ratio sprue : runner : gate, decide whether the system is pressurised or non-pressurised. In a non-pressurised (free-flow) system the sprue is the smallest section and the areas increase downstream, as in the ratio 1 : 2 : 3. The choke is at the base of the sprue, so the system is not pressurised. In a pressurised system the choke is at the gate, the sprue is the largest section, and the downstream channels remain full of metal.

For a simple vertical sprue with head H above the gate, the gate velocity follows Torricelli's relation v = \sqrt{2gH}, and the volumetric flow rate is Q = A_g\sqrt{2gH}. Under the constant-head approximation, the filling time for a mould of volume V is t = V/Q. Example: a gate area of 1 cm^2 and a head of 20 cm with g = 980 cm/s^2 give v \approx 198 cm/s and Q \approx 198 cm^3/s, so a 1000 cm^3 mould fills in about 5 s.

Sintering mechanisms

Sintering bonds powder particles by heating below the melting point of the main constituent, and the driving force is the reduction of surface energy. In solid-state sintering, material moves by surface diffusion, volume diffusion, grain-boundary diffusion or evaporation and condensation, which form and grow necks between particles while the pores shrink. Density rises as the compact shrinks. Because mass is conserved, the volume ratio equals the inverse density ratio, V_s/V_g = \rho_g/\rho_s. For isotropic shrinkage the linear ratio is the cube root of the volume ratio, so linear shrinkage is 1-(\rho_g/\rho_s)^{1/3}. Example: a green density of 80% and a sintered density of 95% of theoretical give a linear shrinkage of about 5.6%.

In liquid-phase sintering, a liquid wets the solid grains, which rearrange and neck together. The equilibrium dihedral angle \theta of the liquid groove is set by the neck geometry, with \sin(\theta/2) = X/D, where X is the neck diameter and D is the grain diameter. A force balance at a solid–solid contact gives \gamma_{SS} = 2\gamma_{SL}\cos(\theta/2), so the solid–solid interfacial energy follows from the solid–liquid value. Example: X/D = 0.3 gives \theta/2 \approx 17.5^\circ and, with \gamma_{SL} = 0.5 J/m^2, \gamma_{SS} \approx 0.95 J/m^2.

Rolling defects

A centre split is a longitudinal crack that runs along the centreline of a rolled strip or bar and separates the material into two portions. It forms when tensile stresses develop at the centre of the section. Such stresses are most likely when the width is large compared with the thickness and when friction at the roll interface is high, because the surface is restrained while the centre is drawn apart. It is recognised as a splitting along the midline, which distinguishes it from surface cracks and from edge cracks that start at the sides of the strip.

• edge crack — a crack that starts at the strip edge, where the cooler and less ductile material is most vulnerable.
• alligatoring — splitting of the ends of an ingot or slab, caused by non-uniform deformation at the ends.

Metal forming processes

Metal forming processes are distinguished by how the force is applied and how the workpiece is constrained. In deep drawing, a blank is pushed by a punch into a die cavity so that a flat sheet becomes a cup, and a blank holder controls wrinkling. In extrusion, a billet inside a container is forced through a die orifice, so the product takes the shape of the orifice under high compressive stress. In rolling, plate or strip is reduced in thickness by passing between rotating cylinders. In open-die forging, the workpiece is compressed between flat platens without enclosing die impressions. Identifying the process from its mechanism, rather than from its outcome, is the key skill.