Firm growth and firm size

This article analyses the growth rates of the complete population of UK-registered firms for the period 2001 to 2005. We estimate Gibrat's law – that growth rates are independent of firm size – by deciles of the firm size distribution. Whether we are able to reject Gibrat's law varies across deciles. We also show how estimates vary according to the measure of firm size, time period and sample selection.

Fatigue crack growth behaviour in molten-metal processed SiC particle-reinforced aluminium alloys

Fatigue crack initiation and subsequent short crack growth behaviour of 2014-5wt%SiC aluminium alloy composites has been examined in 4-point bend loading using smooth bar specimens. The growth rates of long fatigue cracks have also been measured at different stress ratios using pre-cracked specimens. The distributions of SiC particles and of coarse constituent particles in the matrix (which arise as a result of the molten-metal processing and relatively slow cooling rate) have been investigated. Preferential crack initiation sites were found to be SiC-matrix interfaces, SiC particles associated with constituent particles and the coarse constituent particles themselves. For microstructurally short cracks the dispersed SiC particles also act as temporary crack arresters. In the long crack growth tests, higher fatigue crack growth rates were obtained than for monolithic alloys. This effect is attributed to the contribution of void formation, due to the decohesion of SiC particles, to the fatigue crack growth process in the composite. Above crack depths of about 200 μm 'short' crack growth rates were in good agreement with the long crack data, showing a Pris exponent, m = 4 in both cases. For the long crack and short crack growth tests little effect of specimen orientation and grain size was observed on fatigue crack growth rates, but, specimen orientation affected the toughness. No effect of stress ratio in the range R = 0.2-0.5 was seen for long crack data in the Paris region.

The influence of ageing on fatigue crack growth in SiC-particulate reinforced 8090

A study of the influence of SiC-particulate reinforcement on ageing and subsequent fatigue crack growth resistance in a powder metallurgy 8090 aluminium alloy-SiC composite has been made. Macroscopic hardness measurements revealed that ageing at 170°C in the composite is accelerated with respect to the unreinforced alloy, though TEM studies indicate that this is not due to the enhanced precipitation of S′. Fatigue crack growth rates in the naturally aged condition of the composite and unreinforced matrix are similar at low to medium values of ΔK, but diverge above ≈ 8 MPa√m owing to the lower fracture toughness of the composite. As a result of the presence of the reinforcement, planar slip in the composite is suppressed and facetted crack growth is not observed. Ageing at or above 170°C has a deleterious effect on fatigue crack growth. Increased ageing time decreases the roughness of the fracture path at higher growth rates. These effect are though to be due to microstructural changes occurring at or near to the SiC/matrix interfaces, providing sites for static mode failure mechanisms to operate. This suggestion is supported by the observation that as ΔK increases, crack growth rates become Kmax dependent, implying the crack growth rate is strongly influenced by static modes.

Hydrogen embrittlement contributions to fatigue crack growth in a structural steel

The detrimental effects of a hydrogen atmosphere on the fatigue resistance of BS 4360 steel have been assessed by a comparison of crack growth rates in air and hydrogen at a low cycling frequency (0.1Hz), and at a number of temperature (25, 50 and 80 °C). The crack propagation rates in air are almost independent of temperature over this range, but those measured in hydrogen differ by more than an order of magnitude between 25 and 80 °C. The greatest enhancement is seen at 25 °C and at high values of ΔK, the maximum occurring between 40–45 MPa √m at each temperature. There is little hydrogen contribution to crack growth at values of ΔK below 20 MPa √m for R = 0.1. The enhancement of crack growth rates is reflected by the presence of ‘quasi-cleavage’ facets on the fatigue fracture surfaces of specimens tested in hydrogen. These are most apparent where the greatest increases in growth rate are recorded. The facets show linear markings, which run both parallel and perpendicular to the direction of crack growth. The former are analogous to the ‘river’ lines noted on brittle cleavage facets, and reflect the propagation direction. The latter are more unusual, and indicate that facet formation by hydrogen embrittlement during fatigue is a step-wise process.

Residual stress effects during near-threshold fatigue crack growth

The fatigue crack propagation behaviour of a low alloy, boron-containing steel has been examined after austenitizing at 900°C or 1250°C and tempering at a range of temperatures up to 400°C. Fatigue threshold values were found to vary with austenitizing and tempering treatment in a range between 3.3 to 6 MPa √m when tested at a stress ratio (R) of 0.2. Crack propagation rates in the Paris regime were insensitive to heat treatment variations. The crack propagation path was essentially transgranular in all conditions with small regions of intergranular facets appearing at growth rates around the knee of the da/dN vs ΔK curve. The crack front shape showed marked retardation in the centre of the specimen at low tempering temperatures. Experimental determinations and computer predictions of residual stress levels in the specimens indicated that this was due to a central residual compressive stress resulting from differential cooling rates and the volume change associated with the martensite transformation. The results are discussed in terms of microstructural and residual stress effects on fatigue behaviour. © 1987.

Temperature effects on fatigue thresholds and structure sensitive crack growth in a nickel-base superalloy

Fatigue thresholds and slow crack growth rates have been measured in a powder formed nickel-base superalloy from room temperature to 600°C. Two grain sizes were investigated: 5-12 μm and 50 μm. It is shown that the threshold increases with grain size, and the difference is most pronounced at room temperature. Although crack growth rates increase with temperature in both microstructures, the threshold is only temperature dependent in the material with the larger grain size. It is also only in the latter that the room temperature threshold falls when the load ratio is increased from 0.1 to 0.5. At 600°C the higher load ratio causes a 20% reduction in the threshold irrespective of grain size. The results are discussed in terms of surface roughness and oxide-induced crack closure, the former being critically related to the type of crystallographic crack growth, which is in turn shown to be both temperature and stress intensity dependent. © 1983.

Surface damage and near-threshold fatigue crack growth in a Ni-base superalloy in vacuum

Fatigue crack growth rate tests have been performed on Nimonic AP1, a powder formed Ni-base superalloy, in air and vacuum at room temperature. These show that threshold values are higher, and near-threshold (faceted) crack growth rates are lower, in vacuum than in air, although at high growth rates, in the “structure-insensitive” regime, R-ratio and a dilute environment have little effect. Changing the R-ratio from 0.1 to 0.5 in vacuum does not alter near-threshold crack growth rates very much, despite more extensive secondary cracking being noticeable at R= 0.5. In vacuum, rewelding occurs at contact points across the crack as ΔK falls. This leads to the production of extensive fracture surface damage and bulky fretting debris, and is thought to be a significant contributory factor to the observed increase in threshold values.

Effects of microstructure on long and short crack growth in nickel base superalloys

The use of engineering materials in critical applications necessitates the accurate prediction of component lifetime for inspection and renewal purposes. In fatigue limited situations, it is necessary to be able to predict the growth rates of cracks from initiation at a defect through to final fracture. To this end, fatigue crack growth data are presented for different microstructures of typical nickel base superalloys used in gas turbine engines. Crack growth behaviour throughout the life history of the crack, i.e. from the short crack through to the long crack propagation regime, is described for each microstructural condition and discussed in terms of current theories of fatigue crack propagation.

Growth of short fatigue cracks in titanium alloys

The initiation and early propagation of short fatigue cracks has been studied in detail in two alpha / beta titanium alloys as a function of microstructure. Detailed metallography is presented relating short crack growth rates to the microstructural features present. The work shows the significant differences in short crack propagation rates which can be achieved by microstructural changes within a single alloy.

Lichen growth and lichenometry

Lichenometry is one of the most widely used methods available for dating the surface age of various substrata including rock surfaces, boulders, walls, and archaeological remains. It depends on the assumption that if the lag time before colonisation of a substratum by a lichen is known and lichen age can be estimated, then a minimum date can be obtained by measuring the diameter (or another property related to size) of the largest lichen at the site. Lichen age can be determined by variety of methods including calibrating lichen size against surfaces of known age (‘indirect lichenometry’), by constructing a growth rate-size curve from direct measurement of lichen growth (‘direct lichenometry’), using radio-carbon (RC) dating, and from lichen ‘growth rings’. This chapter describes: (1) lichen growth rates and longevity, (2) methods of estimating lichen age, (3) the methodology of lichenometry and (4) applications of lichenometry. Despite its limitations, lichenometry is likely to continue to play an important role in dating a variety of surfaces and also in providing data that contribute to the debate regarding global warming and climate change.