Numerical analysis of hot deep drawing of din 27MNCRB5 steel sheets under controlled stretching

Hot stamping has been widely studied and increasingly applied in the automotive industry. This process is characterized by its ability to stamp high strength steels, yielding products with high mechanical strength, thus reducing the weight of stamped components and therefore the vehicles weight. It also demands less energy because steel sheets are heated by induction, more efficient than electric furnaces. With controlled stretching it is possible to manufacture thinner stamped parts with high mechanical strength, therefore it is necessary to know the formability limits to prevent failure and achieve the largest possible thickness reduction. In this work the hot formability of DIN 27MnCrB5 steel sheets under stretching conditions was evaluated by numerical simulation with the finite element software Forge2008. The numerical results were compared to experimental results. Initially hot tensile tests were simulated to define the strain rate in different regions of the sample and to evaluate the deformation at fracture. For tests at 700, 800 and 900ºC it was found that the strain rates vary from 0.01 to 0.5 s-1. Experimental tensile tests were also carried out with the same conditions as simulated. Both simulation and experiments presented very similar results for the ultimate tensile strength, and therefore it was possible to assume the experimental fracture strain as a consistent input for the numerical models. With the results of the tensile tests, hot Nakazima tests were simulated to evaluate the highest dome which could be formed without failure risks caused by sheet thickness thinning. The simulation results were validated by experimental tests, and as a result, a new numerical strategy was elaborated to define the hot formability based on the plastic instability and necking localization as a function of the stamping temperature and blank dimensions

LEVEL THEORY, PART 3: A BOOLEAN ALGEBRA OF SETS ARRANGED IN WELL-ORDERED LEVELS

On a very natural image of sets, every set has an absolute complement. The ordinary cumulative hierarchy dismisses this idea outright. But we can rectify this, whilst retaining classical logic. Indeed, we can develop a boolean algebra of sets arranged in well-ordered levels. I show this by presenting Boolean Level Theory, which fuses ordinary Level Theory (from Part 1) with ideas due to Thomas Forster, Alonzo Church, and Urs Oswald. BLT neatly implement Conway’s games and surr

Hilary Putnam on Logic and Mathematics, edited by Geoffrey Hellman and Roy T. Cook

Putnam’s most famous contribution to mathematical logic was his role in investigating Hilbert’s Tenth Problem: Putnam is the ‘P’ in the MRDP Theorem. This volume, though, focuses mostly on his work on the philosophy of logic and mathematics. It is a somewhat bumpy ride. Of the twelve papers, two scarcely mention Putnam. Three others focus primarily on Putnam’s ‘Mathematics without Foundations’ (1967), but with no interplay between them. The remaining seven papers apparently tackle unrelated themes. Some of this disjointedness would doubtless have been addressed if Putnam had been able to compose his replies to these papers; sadly, he died before this was possible. In this review, I shall do my best to tease out some connections between the papers; and there are some really interesting connections to be made. Ultimately, though, my review will be only a little less bumpy than the volume itself

Other minds and God: Russell and Stout on James and Schiller

In 1907–8, Russell and Stout presented an objection against James and Schiller, to which both James and Schiller replied. In this paper, I shall revisit their transatlantic exchange. Doing so will yield a better understanding of Schiller’s relationship to a worryingly solipsistic brand of phenomenalism. It will also allow us to appreciate a crucial difference between Schiller and James; a difference which James explicitly downplayed

LEVEL THEORY, PART 2: AXIOMATIZING THE BARE IDEA OF A POTENTIAL HIERARCHY

Potentialists think that the concept of set is importantly modal. Using tensed language as an heuristic, the following bare-bones story introduces the idea of a potential hierarchy of sets: ‘Always: for any sets that existed, there is a set whose members are exactly those sets; there are no other sets.’ Surprisingly, this story already guarantees well-foundedness and persistence. Moreover, if we assume that time is linear, the ensuing modal set theory is almost definitionally equivalent with non-modal set theories; specifically, with Level Theory, as developed in Part 1

Ontology after Carnap

Ontology after Carnap focusses on metaontology in the light of recent interest in Carnap’s ‘Empiricism, Semantics and Ontology’. That paper is at the centre of things, as it is where Carnap formulates his internal/external dichotomy. If you haven’t already encountered the dichotomy, then neither Ontology after Carnap, nor this review, is for you. My aim in this review is to try to tease out some of the book’s themes, thereby giving some sense of contemporary neo-Carnapianism

Every Now and Then, no-futurism faces no sceptical problems

Tallant (2007) challenges my recent defence of no-futurism (Button 2006), but he does not discuss the key to that defence: that no-futurism's primitive relation ‘x is real-as-of y’ is not symmetric. I shall therefore answer Tallant's challenge in the same way as I originally defended no-futurism. Doing so allows me to clarify what no-futurists should believe and to supply a variety of semantic principles for no-futurism. It also shows why no-futurists have nothing to fear from sceptical challenges. This is not to say that no-futurism has no weaknesses, however, and I conclude by suggesting where attacks on no-futurism would be better targeted