Drying Shrinkage (Ceramic)
Compute the linear drying shrinkage of a ceramic piece, DS = (L_wet − L_dry)/L_wet·100%, the size reduction as it loses the forming water before firing. The water that separated the clay particles evaporates and they draw together. Excessive or non-uniform drying shrinkage causes cracks and warping — which is why drying is slow and controlled. Enter the wet and dry lengths.
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Drying shrinkage (ceramic)
Before it reaches the kiln, a freshly formed ceramic piece (pressed, extruded or slip cast) is full of water — and as it dries, it shrinks. Drying shrinkage DS = (L_wet − L_dry)/L_wet·100% measures that reduction, which happens through an elegant mechanism: the flat clay particles are held apart by thin water films; as the water at the surface evaporates, surface tension pulls the particles against one another, bringing them closer — and the piece shrinks while the water that separated them vanishes. This shrinking stage carries on until the particles touch (the 'Bigot point'), beyond which the piece shrinks no further and merely loses the remaining water from the pores already formed (with no further change in size). The great hazard of drying is the gradient: when the surface dries and shrinks much faster than the interior (still wet and still expanded), stresses arise that cause cracking, warping and even bursting of the piece. That is why industrial drying is slow and controlled, in dryers with graduated humidity and temperature, and very plastic clays (which shrink a great deal) are usually 'leaned' with grog or sand to cut the shrinkage and the risk of cracking. Drying shrinkage, added to firing shrinkage, gives the total shrinkage that the mould offsets. Enter the wet length and the dry length.
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Total Shrinkage (Ceramic)
Compute the total linear shrinkage of a ceramic piece, TS = (L_wet − L_fired)/L_wet·100%, combining the drying and firing effects from the formed piece to the final product. It is the shrinkage the mold designer must compensate for: the cavity must be larger than the final piece by the total shrinkage, so the fired piece comes out at the exact size. Enter the wet (formed) and fired (final) lengths.
Loss on Ignition (Ceramic)
Compute the loss on ignition (LOI) of a ceramic raw material, LOI = (mass before − mass after ignition)/mass before·100%, the mass lost during heating at high temperature. It corresponds to the release of combined water (clay minerals), the burning of organic matter and the decomposition of carbonates (releasing CO₂). A high LOI indicates much clay/volatile matter and requires care to avoid defects (bubbles, cracks). Enter the mass before and after ignition.
Concrete Shrinkage Loss
Calculate the prestress loss from concrete shrinkage, Δσ = ε_cs·E_s, from the shrinkage strain ε_cs (dimensionless) and the steel modulus E_s (MPa). Shrinkage is the volume reduction concrete undergoes over time as it LOSES water by evaporation (drying shrinkage) and through cement hydration reactions (autogenous shrinkage), independent of loading. When the concrete of a prestressed member shrinks (shortens), the bonded steel tendon shortens too — and shortening, it LOSES tension, exactly as in elastic-shortening loss, except here the shortening is from shrinkage and occurs SLOWLY over months and years. The loss is simply the shrinkage strain times the steel modulus (the stress that shortening 'steals' from the tendon). The shrinkage strain ε_cs is typically 0.0002-0.0005 (200-500 microstrains) and depends on ambient humidity (drier = more shrinkage), member dimensions (thin members shrink more, losing water faster), mix and time. It is one of the three time-dependent losses (with creep and relaxation) reducing prestress over the structure's life. Enter the shrinkage strain and the steel modulus.
Firing Shrinkage (Ceramic)
Compute the linear firing shrinkage of a ceramic piece, FS = (L_dry − L_fired)/L_dry·100%, the size reduction during sintering in the kiln, when pores close and particles draw together. It is a critical dimensional-control parameter: porcelain tiles shrink a lot (~7%), while porous ceramics shrink little. Variations in shrinkage cause product miscalibration. Enter the dry and fired lengths.
Weld Cooling Time t8/5
Computes how long the heat affected zone takes to cool from 800 °C to 500 °C, the t8/5 parameter of EN 1011-2, from the heat input, the preheat temperature and the joint shape factor. The formula multiplies the term (6700 − 5 × preheat temperature) by the heat input, by the difference between the reciprocals of (500 − T₀) and (800 − T₀), and by the shape factor tabulated in the standard, which is 1.0 for a bead deposited on a plate and drops to about 0.9 for a butt weld and 0.67 for a fillet weld on a T-joint. Austenite decomposes in that range, so t8/5 decides the microstructure of the joint: cooling too fast forms martensite and opens the door to cold cracking, cooling too slowly coarsens the grain and destroys impact toughness, and most structural steels call for something between 5 and 25 seconds. The three-dimensional heat flow equation was adopted, valid when the plate is thick relative to the weld bead; in thin plate the flow is two-dimensional and t8/5 grows with the square of the heat input rather than in proportion to it. Enter the heat input, the preheat temperature and the joint shape factor.
Bulk Density (Ceramic)
Compute the bulk (apparent) density of a ceramic, BD = dry mass/(wet mass − immersed mass), by Archimedes' method, considering the total piece volume (including pores). It is an indicator of the densification achieved in firing: higher bulk density means fewer pores and generally higher strength. Water density (1 g/cm³) is used in the hydrostatic weighing. Enter the dry, wet and immersed masses.
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